{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 8: HYDRAULIC PUMPS"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.10: EXIT_BLADE_ANGLE.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Ihl=3//Head loss in impeller in m\n",
"Cr2=4.64//Flow velocity through impeller at outlet in m/s\n",
"U2=30//Blade outlet speed in m/s\n",
"dPi=35.3//Difference in pressure gauge readings at impeller inlet and outlet in m of water\n",
"Pg=4.7//Pressure gain in the casing in m of water \n",
"n=0.385//Part of absolute kinetic energy converted into pressure gain\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"d=1000//Density of water in kg/m^3\n",
"ss=0.85//Slip coefficient\n",
"\n",
"//calculations\n",
"Kei=Pg/n//Kinetic energy at impeller exit in m/s\n",
"C2=((Kei)*2*g)^(1/2)//Velocity at impeller exit in m/s\n",
"Cx22=(C2^2-Cr2^2)^(1/2)//Absolute whirl component at outlet with fliud slip in m/s\n",
"Cx2=Cx22/ss//Ideal absolute whirl velocity in m/s\n",
"b22=atand(Cr2/(U2-Cx2))//Blade angle at exit in degree\n",
"Wm=ss*U2*Cx2//Euler work input in J/kg\n",
"nm=dPi/(U2*Cx22/g)//Manometric efficiency\n",
"dP=(U2*Cx22/g)-(Ihl)-(C2^2/(2*g))//Pressure rise in impeller in m\n",
"\n",
"//output\n",
"printf('(a)\n    Exit blade angle is %3.2f degree\n    Euler work input is %3.2f J/kg\n(b)Manometric efficiency is %3.4f\n(c)Pressure rise in the impeller is %3.3f m',b22,Wm,nm,dP)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.11: VOLUME_FLOW_RATE_THROUGH_IMPELLER.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"r1=0.051//Eye radius of the impeller in m\n",
"D2=0.406//Outer diameter of the impeller in m\n",
"b11=(90-75)//Inlet blade angle measured from tangential flow direction in degree\n",
"b22=(90-83)//Outlet blade angle measured from tangential flow direction in degree\n",
"b=0.064//Blade depth in m\n",
"Cx1=0//Inlet whirl velocity in m/s\n",
"nh=0.89//Hydraulic efficiency \n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"d=1000//Density of water in kg/m^3\n",
"N=900//Rotating speed of impeller in rpm\n",
"\n",
"//calculations\n",
"w=(2*3.1415*N)/60//Angular velocity at inlet in rad/s\n",
"U1=(w*r1)//Inlet tangential impeller velocity in m/s\n",
"C1=U1*tand(b11)//Velocity at impeller inlet in m/s\n",
"A=2*3.1415*r1*b//Area of flow through the pump in m^2\n",
"Cr1=C1//Flow velocity through impeller at inlet in m/s\n",
"Q=A*Cr1//Volume flow through the pump in m^3/s\n",
"r2=D2/2//Outer radius of the impeller in m\n",
"Cr2=(r1*Cr1)/r2//Flow velocity through impeller at outlet in m/s\n",
"U2=w*r2//Outlet tangential impeller velocity in m/s\n",
"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n",
"E=(U2/g)*(U2-Wx2)//Theoretical head developed in m\n",
"Hm=nh*E//Total stagnation head developed by the pump in m\n",
"dP021=Hm*d*g*10^-3//Total pressure head coefficient in kPa\n",
"Cx2=U2-(Cr2/tand(b22))//Absolute whirl velocity in m/s\n",
"C2=(Cr2^2+Cx2^2)^(1/2)//Velocity at impeller exit in m/s\n",
"dP21=(Hm-(((C2^2)-(C1^2))/(2*g)))*d*g*10^-3//The static pressure head in kPa\n",
"P=d*g*Q*Hm*10^-3//Power given to the fluid in kW\n",
"Ps=P/nh//Input power to impeller in kW\n",
"\n",
"//output\n",
"printf('(a)Volume flow rate through the impeller is %3.4f m^3/s\n(b)\n    stagnation pressure rise across the impeller is %3.1f kPa\n    Static pressure rise across the impeller is %3.1f kPa\n(c)Power given to fluid is %3.2f kW\n(d)Input power to impeller is %3.2f kW',Q,dP021,dP21,P,Ps)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.12: IMPELLER_DIAMETER.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Q=0.04//Discharge of the pump design in m^3/s\n",
"Ns=0.075//Specific speed in rev\n",
"b22=(180-120)//Outlet angle with the normal in degree\n",
"H=35//Distance to which pumping of water is done in m\n",
"Dp=0.15//Diameter of suction and delivery pipes in m\n",
"L=40//Combined length of suction and delivery pipes in m\n",
"WD=1/10//Width to diameter ratio at outlet of impeller \n",
"f=0.005//Friction factor \n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"nh=0.76//Hydraulic effficiency neglecting the slip\n",
"n=0.06//Percentage occupied by blades on circumference area\n",
"\n",
"//calculations\n",
"A=(3.1415/4)*(Dp^2)//Area of flow in pipe in m^2\n",
"V=Q/A//Velocity in the pipes in m/s\n",
"OL=3*V^2/(2*g)//Other loses in the pipes in m\n",
"TL=(4*f*L*V^2/(2*g*Dp))+(OL)//Total loses in a pipe in m\n",
"TH=TL+H//Total required head in m\n",
"N=(Ns*((g*H)^(3/4)))/((Q)^(1/2))//The speed of the pump in rev/s\n",
"Ao=3.1415*WD*(1-n)//Flow area perpendicular to impeller outlet periphery in terms of D^2 in m^2            In this the area is calculated using only the circumferential area without blades\n",
"Cr2=Q/Ao//Flow velocity through impeller at outlet in m/s\n",
"U2=3.1415*N//Outlet tangential impeller velocity in m/s in terms of D\n",
"Cx2=(g*H)/(U2*nh)//Absolute whirl velocity in m/s\n",
"\n",
"//The following steps are for calculating the cubic root equation in D\n",
"//This is obtained by solving    tand(b22)=(Cr2/(Cx2-U2))   all values are substituted in terms of D\n",
"//The final equation which is obtained is      D^3-0.0495D+0.0008=0\n",
"//The above equation is solved using the following formulae\n",
"\n",
"a=0//Coefficient of D^2 in the above equation\n",
"b=-0.0511//Coefficient of D in the above equation\n",
"c=0.00083//Constant term in above equation\n",
"q=c+((2*(a^3))/27)-(a*b/3)//Constant in solving the cubic equation\n",
"p=((3*b)-(a^2))/3//Constant in solving the cubic equation\n",
"d=(p/2)^2+(q/3)^3//Constant in solving the cubic equation\n",
"u=((-q/2)+(d^(1/2)))^(1/3)//Constant in solving the cubic equation\n",
"v=((-q/2)-(d^(1/2)))^(1/3)//Constant in solving the cubic equation\n",
"D=(u+v)/2//Impeller diameter in m\n",
"\n",
"//output\n",
"printf('The pump impeller diameter is %3.3f m',D)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.13: SPECIFIC_SPEED.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"N=2875//Speed of the pump in rpm \n",
"Q=57.2/3600//Discharge of the pump in m^3/s\n",
"Hm=42.1//Total head developed by the pump in m\n",
"d=1000//Density of the water in kg/m^3\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"n=0.76//Efficiency of the pump\n",
"\n",
"//calculations\n",
"Ns=(N*Q^(1/2))/(Hm^(3/4))//Specific speed of the pump \n",
"P=((d*g*Q*Hm)/n)*10^-3//Power input in kW\n",
"\n",
"//calculations\n",
"printf('(a)Specific speed of the pump is %3.f\n(b)Power input is %3.3f kW',Ns,P)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.14: MANOMETRIC_EFFICIENCY.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"D1=0.6//Inlet impeller diameter in m\n",
"D2=1.2//Outlet impeller diameter in m\n",
"Cr2=2.5//Radial flow velocity in m/s\n",
"N=200//Running speed of the pump in rpm\n",
"Q=1.88//Discharge of the pump in m^3/s\n",
"Hm=6//Head which the pump has to overcome in m\n",
"b22=26//Vane angle at exit at tangent to impeller in degree\n",
"d=1000//Density of the water in kg/m^3\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"U2=(3.1415*D2*N)/60//Outlet tangential impeller velocity in m/s\n",
"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n",
"Cx2=U2-Wx2//Absolute whirl velocity in m/s\n",
"nm=(Hm/(U2*Cx2/g))//Manometric efficiency \n",
"Nls=((2*g*Hm*60^2)/((3.1415^2)*((1.2^2)-(0.6^2))))^(1/2)//Least starting speed of the pump in rpm\n",
"\n",
"//output\n",
"printf('(1)Manometric efficiency is %3.3f\n(2)Least speed to start the pump is %3.2f rpm',nm,Nls)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.15: HYDRAULIC_OR_MANOMETRIC_EFFICIENCY.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"D2=1.25//External diameter of the impeller in m\n",
"D1=0.5//Internal diameter of the impeller in m\n",
"Q=2//Discharge of the pump in m^3/s\n",
"Hm=16//Head over which pump has to operate in m\n",
"N=300//Running speed of the pump in rpm\n",
"b22=30//Angle at which vanes are curved back in degree\n",
"Cr1=2.5//Flow velocity through impeller at inlet in m/s\n",
"Cr2=Cr1//Flow velocity through impeller at outlet in m/s\n",
"d=1000//Density of the water in kg/m^3\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"U2=(3.1415*D2*N)/60//Outlet tangential impeller velocity in m/s\n",
"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n",
"Cx2=U2-Wx2//Absolute whirl velocity in m/s\n",
"nm=(Hm*g)/(U2*Cx2)//Manometric or hydraulic efficiency\n",
"m=d*Q//Mass flow rate of water in kg/s\n",
"W=m*U2*Cx2*10^-3//Fluid power developed by the impeller in kW\n",
"Ps=W//Power required by the pump in kW neglecting mechanical loses\n",
"Nls=((2*g*Hm)/(((3.1415/60)^2)*(D2^2-D1^2)))^(1/2)//Minimum starting speed of the pump in rpm\n",
"\n",
"//output\n",
"printf('(a)Manometric or hydraulic efficiency is %3.3f \n(b)Power required by the pump is %3.2f kW\n(c)Minimum starting speed of the pump is %3.1f rpm',nm,Ps,Nls)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.16: HEAT_GENERATED_BY_PUMP.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"n=3//Number of stages \n",
"D2=0.4//Outlet impeller diameter in m\n",
"b2=0.02//Outlet impeller width in m\n",
"b22=45//Backward vanes angle at outlet in degree\n",
"dA=0.1//Reduction in circumferential area\n",
"nm=0.9//Manometric efficiency of the pump\n",
"Q=0.05//Discharge of the pump in m^3/s\n",
"N=1000//Running speed of the pump in rpm\n",
"n0=0.8//Overall efficiency of the pump\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"d=1000//Density of water in kg/m^3\n",
"\n",
"//calculations\n",
"A2=(1-dA)*3.1415*D2*b2//Area of flow at outlet in m^2\n",
"Cr2=Q/A2//Flow velocity through impeller at outlet in m/s\n",
"U2=(3.1415*D2*N)/60//Outlet impeller tangential velocity in m/s\n",
"Wx2=Cr2//Exit relative velocity in m/s as tand(b22)=1\n",
"Cx2=U2-Wx2//Absolute whirl velocity in m/s\n",
"Hm=(nm*U2*Cx2)/g//Head over which pump has to operate in m\n",
"H=n*Hm//Total head generated by the pump in m\n",
"P=d*g*Q*Hm*n//Power output from the pump in W\n",
"Ps=P/n0*10^-3//Shaft power input in kW\n",
"\n",
"//output\n",
"printf('(1)The head generated by the pump is %3.2f m\n(2)Shaft power input is %3.3f kW',H,Ps)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.17: NUMBER_OF_PUMPS.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"H=156//Total head operated by the pumps in m\n",
"N=1000//Running speed of the pump in rpm\n",
"Ns=20//Specific speed of each pump \n",
"Q=0.150//Discharge of the pump in m^3/s\n",
"\n",
"//calculations\n",
"Hm=((N*(Q)^(1/2))/(Ns))^(4/3)//Head developed by each pump in m\n",
"n=H/Hm//Number of pumps\n",
"\n",
"//output\n",
"printf('The number of pumps are %3.f',n)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.18: IMPELLER_DIAMETER_AND_NUMBER_OF_STAGES.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Q1=120//Discharge of each of the multi stage pump in parallel in first case in m^3/s\n",
"Q2=450//Discharge of the multi stage pump in second case in m^3/s\n",
"H1=16//Head of each stage in first case in m\n",
"D1=0.15//Diameter of impeller in first case in m\n",
"H=140//Total head developed by all pumps in second case in m\n",
"N1=1500//Running speed of the pump in rpm in first case\n",
"N2=1200//Running speed of the pump in rpm in second case\n",
"//calculations\n",
"H2=H1*((Q2/Q1)*((N2/N1)^2))^(4/6)//Head of each stage in second case in m\n",
"n=H/H2//Number of stages in second case \n",
"D2=D1*(((N1/N2)^(2))*(H2/H1))^(1/2)//Diameter of impeller in second case in m\n",
"\n",
"//output\n",
"printf('(a)number of stages required is %3.f\n(b)Diameter of impeller in the second case is %3.2f m',n,D2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.19: CAVITATION_PARAMETER.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"H=36//Initial total head of the pump in m\n",
"Q1=0.05//Initial discharge of the pump in m^3/s\n",
"H2=3.5//Sum of static pressure and velocity head at inlet in m\n",
"P01=0.75//Atmospheric pressure initially in m of Hg\n",
"Pvap1=1.8*10^3//Vapour pressure of water initially in Pa\n",
"Pvap2=830//Vapour pressure of water finanlly in Pa\n",
"P02=0.62//Atmospheric pressure finally in m of Hg\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"dW=1000//Density of water in kg/m^3\n",
"dHg=13.6//Density of mercury in kg/m^3\n",
"\n",
"//calculations\n",
"NPSH=H2-((Pvap1)/(dW*g))//Net positive suction head in m\n",
"s=NPSH/H//Cavitation parameter when pump dvelops same total head and discharge \n",
"dH1=(P01*dHg)-(s*H)-(Pvap1/(dW*g))//The height reduced in initial condition above supply in m\n",
"dH2=(P02*dHg)-(s*H)-(Pvap2/(dW*g))//The height reduced in final condition above supply in m\n",
"Z=dH1-dH2//The total height which the pump must be lowered at new location in m\n",
"\n",
"//output\n",
"printf('(a)The cavitation parameter is %3.4f\n(b)\n    The height reduced in initial condition above supply is %3.1f m\n    The height reduced in final condition above supply is %3.2f m\n    The total height which the pump must be lowered at new location is %3.2f m',s,dH1,dH2,Z)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.1: TORQUE_DELIVERED.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"D=1.3//Diameter of the pump in m\n",
"Q=3.5/60//Discharge of water by pump in m^3/s\n",
"U2=10//Tip speed of pump in m/s\n",
"Cr2=1.6//Flow velocity of water in pump in m/s\n",
"b2=30//Outlet blade angle tangent to impeller periphery in degree\n",
"Cx1=0//Whirl velocity at inlet in m/s\n",
"U=10//Tip speed of pump in m/s\n",
"d=1000//Density of water in kg/m^3\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"Wx2=Cr2/tand(b2)//Exit relative velocity in m/s\n",
"E=(U2/g)*(U2-(Wx2))//Euler head in m or W/(N/S)\n",
"m=d*Q//Mass flow rate of water in kg/s\n",
"W=E*m*g//Power delivered in W\n",
"r=D/2//Radius of the pump in m\n",
"T=W/(U/r)//Torque delivered in Nm\n",
"\n",
"//output\n",
"printf('Torque delivered by the impeller is %3.1f Nm',T)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.20: VANE_ANGLE_AT_ENTRY.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Dt=1//Impeller outlet diameter in m\n",
"Dh=0.5//Diameter of the boss in m\n",
"Ns=38//Specific speed of the pump \n",
"Ca=2//Velocity of the flow in m/s\n",
"H=6//Head which the pump has to drive in m\n",
"\n",
"//calculations\n",
"A=(3.1415/4)*(Dt^2-Dh^2)//Area of flow in m^2\n",
"Q=A*Ca//Discharge of the pump in m^3/s\n",
"N=(Ns*H^(3/4))/(Q^(1/2))//Pump speed in rpm\n",
"U1=(3.1415*Dh*N)/60//Blade inlet speed in m/s\n",
"b1=atand(Ca/U1)//Vane angle at the entry of the pump when the flow is axial at inlet in degree\n",
"\n",
"//output\n",
"printf('(a)Pump speed is %3.3f rpm\n(b)Vane angle at the entry of the pump when the flow is axial at inlet is %3.2f degree',N,b1)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.21: PUMP_SPEED.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Q=0.180//Discharge of the pump in m^3/s\n",
"H=2//Head developed by the pump in m\n",
"Ns=250//Specific speed of the pump \n",
"SR=2.4//Speed ratio of the pump\n",
"FR=0.5//Flow ratio of the pump\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"N=(Ns*(H^(3/4)))/(Q^(1/2))//Pump speed in rpm\n",
"U=SR*(2*g*H)^(1/2)//Peripheral velocity in m/s\n",
"D=(60*U)/(3.1415*N)//Runner diameter of the pump in m\n",
"Ca=FR*(2*g*H)^(1/2)//Velocity of flow in m/s\n",
"Dh=((D^2)-(Q*4/(Ca*3.14)))^(1/2)//Boss diameter of the pump in m\n",
"\n",
"//output\n",
"printf('(a)Pump speed is %3.i rpm\n(b)Runner diameter of the pump is %3.2f m\n(c)Boss diameter of the pump is %3.2f m\n',N,D,Dh)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.22: JET_PUMP_EFFICIENCY.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Hs=2.5//Height of the pipe above suction reservoir in m\n",
"H1=18//Height of the pipe below supply reservoir in m\n",
"H=2.7//Total height through which the pump lifts water in m\n",
"Q1=2.75//Discharge of water used from supply reservoir in l/s\n",
"Qt=7.51//Discharge of water totally delivered in l/s\n",
"\n",
"//calculations\n",
"Hd=H-Hs//Height of the pipe from discharge reservoir in m\n",
"Qs=Qt-Q1//Discharge of water in delivery reservoir in l/s\n",
"nj=(Qs/Q1)*((Hs+Hd)/(H1-Hd))//Jet pump efficiency \n",
"\n",
"//output\n",
"printf('The efficiency of the jet pump is %3.3f',nj)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.2: THEORETICAL_HEAD.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"b2=30//Impeller blade angle to the tangent at impeller outlet in degree\n",
"d=0.02//Blade depth in m\n",
"D=0.25//Blade diameter in m\n",
"N=1450//Pump rotation speed in rpm\n",
"Q=0.028//FLow rate of the pump in m^3/s\n",
"sf=0.77//Slip factor \n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"A=3.1415*d*D//Flow area in m^2\n",
"Cr2=Q/A//Flow velocity in m/s\n",
"Wx2=Cr2/tand(b2)//Exit relative velocity in m/s\n",
"U2=(3.14*D*N)/60//Tip speed of pump in m/s\n",
"Cx2=U2-Wx2//Absolute whirl component at exit in m/s\n",
"E=(U2*Cx2)/g//Euler head with no whirl at inlet in m\n",
"Cx21=sf*Cx2//Actual value of component of absolute value in tangential direction in m/s\n",
"Es=sf*E//Theoretical head with slip in m\n",
"Z=(3.145*sind(b2))/((1-sf)*(1-((Cr2/U2)*cotd(b2))))//Number of blades required based on stodola slip factor\n",
"\n",
"//output\n",
"printf('(a)Theoretical head with slip is %3.2f m\n(b)Number of blades required is %3.f',Es,Z)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.3: DISCHARGE.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"D2=0.4//Outer diameter of impeller in m\n",
"b2=0.05//Outlet width of impeller in m\n",
"N=800//Running speed of pump in rpm\n",
"Hm=16//Working head of pump in m\n",
"b22=40//Vane angle at outlet in degree\n",
"nm=0.75//Manometric efficiency \n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"U2=(3.1415*D2*N)/60//Impeller tip speed in m/s\n",
"Cx2=(g*Hm)/(U2*nm)//Absolute whirl component at exit in m/s\n",
"Wx2=U2-Cx2//Exit relative velocity in m/s\n",
"Cr2=Wx2*tand(b22)//Flow velocity of water in pump in m/s\n",
"A=3.14*D2*b2//Area of flow in m^2\n",
"Q=A*Cr2//Discharge of the pump in m^3/s\n",
"\n",
"//output\n",
"printf('The discharge of the pump is %3.4f m^3/s',Q)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.4: VANE_INLET_ANGLE.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"D2D1=2//The ratio of outer and inner diameter \n",
"N=1200//The running speed of pump in rpm\n",
"Hm=75//Total head producing work in m\n",
"Cr1=3//Flow velocity through impeller at inlet in m/s\n",
"Cr2=Cr1//Flow velocity through impeller at outlet in m/s\n",
"b22=30//Vanes set back angle at outlet in degree\n",
"D2=0.6//Outlet diameter of impeller in m\n",
"d=1000//Density of water in kg/m^3\n",
"b2=0.05//Width of impeller at outlet in m\n",
"g=9.81//Acceleartion due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"D1=D2/D2D1//Inlet diameter of impeller in m\n",
"U1=(3.1415*D1*N)/60//Impeller tip speed at inlet in m/s\n",
"b11=atand(Cr1/U1)//Vane angle at inlet in degree\n",
"U2=(3.1415*D2*N)/60//Impeller tip speed at exit in m/s\n",
"A=3.1415*D2*b2//Area of flow in m^2\n",
"Q=A*Cr2//Discharge of the pump in m^/s\n",
"m=d*Q//Mass flow rate of water in kg/s\n",
"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n",
"Cx2=U2-Wx2//Absolute whirl component at exit in m/s\n",
"W=m*U2*Cx2*10^-3//Work done per second in kW\n",
"nm=Hm/((U2*Cx2)/g)//Manometric efficiency \n",
"\n",
"//output\n",
"printf('(a)Vane angle at inlet is %3.3f degree\n(b)Work done per second is %3.2f kW\n(c)Manometric efficiency is %3.4f',b11,W,nm)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.5: ANGLES_AND_EFFICIENCIES.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Q=75//Discharge from the pump in l/s\n",
"D1=0.1//Inlet diameter of the pump in m\n",
"D2=0.29//Outlet diameter of the pump in m \n",
"Hm=30//Total head producing work in m\n",
"N=1750//Speed of the pump in rpm\n",
"b1=0.025//Width of impeller at inlet per side in m\n",
"b2=0.023//Width of impeller at outlet in total in m\n",
"a11=90//The angle made by the entering fluid to impeller in degree\n",
"b22=27//Vanes set back angle at outlet in degree\n",
"Qloss=2.25//Leakage loss in l/s\n",
"ml=1.04//Mechanical loss in kW\n",
"cf=0.87//Contraction factor due to vane thickness \n",
"n0=0.55//Overall efficiency\n",
"d=1000//Density of water in kg/m^3\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"U1=(3.1415*D1*N)/60//Blade inlet speed in m/s\n",
"A1=3.1415*D1*b1*cf*10^3//Area of flow at inlet in m^2\n",
"Qt=Q+Qloss//Total quantity of water handled by pump in l/s\n",
"Qts=Qt/2//Total quantity of water handled by pump per side in l/s\n",
"Cr1=(Qts*10^-3)/(A1*10^-3)//Flow velocity through impeller at inlet in m/s\n",
"b11=atand(Cr1/U1)//Inlet vane angle in degree\n",
"A2=3.1415*D2*(b2/2)*cf*10^3//Area of flow at outlet in m^2 here b2 is calculated per side\n",
"Cr2=Qts/A2//Velocity of flow at outlet in m/s\n",
"U2=(3.1415*D2*N)/60//Peripheral speed at outlet in m/s\n",
"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n",
"Cx2=U2-Wx2//Absolute whirl component at exit in m/s\n",
"a22=atand(Cr2/Cx2)//The absolute water angle at outlet in degree\n",
"C2=Cr2/sind(a22)//Absolute velocity of water at exit in m/s\n",
"nh=Hm/((U2*Cx2)/g)//Manometric efficiency \n",
"nv=Q/Qt//Volumetric efficiency \n",
"SP=(d*g*(Q*10^-3/2)*Hm)/n0*10^-3//Shaft power in kW\n",
"nm=(SP-ml)/SP//Mechanical efficiency \n",
"\n",
"//output\n",
"printf('(a)Inlet vane angle is %3.2f degree\n(b)The absolute water angle is %3.2f degree\n(c)Absolute velocity of water at exit is %3.2f m/s\n(d)Manometric efficiency is %3.3f\n(e)Volumetric efficiency is %3.4f\n(f)Mechanical efficiency is %3.3f',b11,a22,C2,nh,nv,nm)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.6: MANOMETRIC_HEAD_AND_OVERALL_EFFICIENCY.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Hi=0.25//Vaccum gauge reading in m of Hg vaccum\n",
"P0=1.5//Pressure gauge reading in bar\n",
"Z01=0.5//Effective height between gauges in m\n",
"P=22//Power of electric motor in kW\n",
"Di=0.15//Inlet diameter in m\n",
"Do=0.15//Outlet diameter in m\n",
"Q=0.1//Discharge of pump in m^3/s\n",
"dHg=13600//Density of mercury in kg/m^3\n",
"dw=1000//Density of water in kg/m^3\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"Pi=dHg*g*Hi//Inlet pressure in N/m^2 vaccum\n",
"Po=P0*10^5//Outlet pressure in N/m^2\n",
"V0=Q/((3.1415*Do^2)/4)//Velocity of water in delivery pipe in m/s\n",
"Vi=V0//vleocity of water in suction pipe in m/s\n",
"Hm=((Po+Pi)/(dw*g))+((V0^2-Vi^2)/(2*g))+(Z01)//Manometric head in m\n",
"n0=(dw*g*Q*Hm)/(P*10^3)//Overall efficiency \n",
"\n",
"//output\n",
"printf('(a)Manometric head is %3.2f m\n(b)Overall efficiency is %3.3f',Hm,n0)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.7: IMPELLER_DIAMETER.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Hm=20//Head against which work is produced in pump in m\n",
"b22=45//Vanes set back angle at outlet in degree\n",
"N=600//Rotating speed of pump in rpm\n",
"Cr1=2//Flow velocity through impeller at inlet in m/s\n",
"Cr2=Cr1//Flow velocity through impeller at outlet in m/s\n",
"g=9.81//acceleration due to gravity in m/s^2\n",
"\n",
"//calculations\n",
"Wx2=Cr2/tand(b22)//Exit relative velocity in m/s\n",
"U2=(4+(16+(4*3*792.8))^(1/2))/(2*3)//   Blade outlet speed in m/s\n",
"     //The above equation is obtained by solving \n",
"     //Cx2=U2-Wx2     //Absolute whirl component at exit in m/s\n",
"     //C2=(Cx2^2+Cr2^2)^(1/2)    //Absolute velocity of water at exit in m/s\n",
"     //Hm=(U2*Cx2/g)-((C2^2)/(4*g))     //Total head producing work in m\n",
"     //3*(U2^2)-(4*U2)-792.8=0       \n",
"D2=(60*U2)/(3.1415*N)//Impeller diameter in m\n",
"\n",
"//output\n",
"printf('The impeller diameter is %3.4f m',D2)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.8: POWER_REQUIRED.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"n0=0.7//Overall efficiency\n",
"Q=0.025//Discharge of water by the pump in m^3/s\n",
"H=20//Height of supplied by the pump in m\n",
"D=0.1//Diameter of the pump in m\n",
"L=100//Length of the pipe in m\n",
"f=0.012//Friction coefficient \n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"d=1000//Density of water in kg/m^3\n",
"\n",
"//calculations\n",
"V0=Q/((3.1415/4)*D^2)//Velocity of water in the pipe in m/s\n",
"hf0=(4*f*L*V0^2)/(2*g*D)//Loss of head due to friction in pipe in m\n",
"Hm=H+hf0+(V0^2/(2*g))//Manometric head in m\n",
"P=(d*g*Q*Hm)/(n0)*10^-3//Power required to drive the pump in kW\n",
"\n",
"//output\n",
"printf('Power required to drive the pump is %3.2f kW',P)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 8.9: RISE_IN_PRESSURE_IN_THE_IMPELLER.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"//input data\n",
"Q=0.015//Discharge of water in pump in m^3/s\n",
"D1=0.2//Internal diameter of the impeller in m\n",
"D2=0.4//External diameter of the impeller in m\n",
"b1=0.016//Width of impeller at inlet in m\n",
"b2=0.008//Width of impeller at outlet in m\n",
"N=1200//Running speed of the pump in rpm\n",
"b22=30//Impeller vane angle at outlet in degree\n",
"g=9.81//Acceleration due to gravity in m/s^2\n",
"d=1000//Density of water in kg/m^3\n",
"\n",
"//calculations\n",
"printf('From velocity triangles the following values have been deduced')\n",
"a11=90//The absolute water angle at inlet in degree\n",
"Cx1=0//Absolute whirl component at inlet in m/s\n",
"A1=3.1415*D1*b1//Area of flow at inlet in m^2\n",
"Cr1=Q/A1//Flow velocity through impeller at inlet in m/s\n",
"C1=Cr1//Absolute velocity at inlet in m/s\n",
"A2=3.1415*D2*b2//Area of flow at outlet in m^2\n",
"Cr2=Q/A2//Flow velocity through impeller at outlet in m/s\n",
"U2=(3.1415*D2*N)/60//Blade outlet speed in m/s\n",
"Cx2=U2-(Cr2/tand(b22))//Absolute whirl component at outlet in m/s\n",
"C2=(Cx2^2+Cr2^2)^(1/2)//Velocity at impeller exit in m/s\n",
"Ihl=((Cx2*U2)/g)-((C2^2)/(2*g))+((C1^2)/(2*g))//Pressure rise in impeller in m\n",
"\n",
"//output\n",
"printf('\n\nThe rise in pressure in the impeller is %3.3f m',Ihl)"
   ]
   }
],
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			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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