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{
"metadata": {
"name": "",
"signature": "sha256:6ab6ca7ec50b12b4ad5664b1412855d8b1bafd30fee8faf6c1773c772ff215d4"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Chapter13-Fluid Machines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg618"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate Hydraulic Efficiency and Overall Efficiency and Outlet angles of the guide vanes and Rotor blade angle at inlet and oulet\n",
"\n",
"## Maximum hydraulic efficiency occurs for minimum pressure loss, that is, when\n",
"\n",
"## dp1/dQ=2.38Q-1.43=0\n",
"\n",
"Q_opt=1.43/2.38;\n",
"\n",
"p1_min=1.19*Q_opt**2-1.43*Q_opt+0.47; ## MPa\n",
"\n",
"rho=1000.; ## kg/m**3\n",
"g=9.81; ## m/s**2\n",
"w=69.1; ## rad/s\n",
"P=200.*10.**3.; ## W\n",
"Ohm_P=0.565; ## rad\n",
"d=0.5; ## m\n",
"h=0.06; ## m\n",
"\n",
"p1=p1_min*10.**6./(rho*g); ## mH2O, coversion of units\n",
"\n",
"H=(w*P**(1/2.)/(rho**(1/2.)*Ohm_P))**(4/5.)/g;\n",
"\n",
"Hydraulic_efficiency=(H-p1)/H;\n",
"print'%s %.3f %s'%(\"Hydraulic Efficiency =\",Hydraulic_efficiency,\"\")\n",
"\n",
"\n",
"Overall_efficiency=P/(Q_opt*rho*g*H);\n",
"print'%s %.3f %s'%(\"Overall Efficiency =\",Overall_efficiency,\"\")\n",
"\n",
"\n",
"H_Euler=H-p1;\n",
"\n",
"u1=w*0.25;\n",
"v_w1=g*H_Euler/u1;\n",
"A=math.pi*d*h*0.95; \n",
"v_r=Q_opt/A;\n",
"\n",
"alpha1=math.atan(v_r/v_w1);\n",
"print'%s %.3f %s'%(\"Outlet angles of the guide vanes =\",alpha1,\"degrees\")\n",
"\n",
"beta1=math.atan(v_r/(v_w1-u1));\n",
"print'%s %.2f %s'%(\"Rotor blade angle at inlet =\",beta1,\"degrees\")\n",
"\n",
"u2=w*0.325/2;\n",
"beta2=math.atan(v_r/u2);\n",
"print'%s %.3f %s'%(\"Rotor blade angle at outlet =\",beta2,\"degrees\")\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hydraulic Efficiency = 0.896 \n",
"Overall Efficiency = 0.855 \n",
"Outlet angles of the guide vanes = 0.321 degrees\n",
"Rotor blade angle at inlet = 1.16 degrees\n",
"Rotor blade angle at outlet = 0.539 degrees\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg622"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate Overall efficiency and Limiting value for the height of the draft tube above\n",
"w=6.25;\n",
"D=0.75; ## m\n",
"gv_angle=15; ## guide vane angle in degrees\n",
"g=9.81; ## m/s^2\n",
"H=27.5; ## m\n",
"A1=0.2; ## m^2\n",
"rho=1000.; ## kg/m^3\n",
"p_atm=101.3*10**3.;\n",
"p_min=35.*10.**3.;\n",
"\n",
"u1=math.pi*w*D;\n",
"v1=u1*math.sin(105.)/math.sin(60.);\n",
"v_r1=v1*math.sin(gv_angle);\n",
"v_w1=v1*math.cos(gv_angle);\n",
"v_w2=0.;\n",
"\n",
"n_hydraulic=u1*v_w1/g/H;\n",
"\n",
"n_overall=0.97*n_hydraulic;\n",
"print'%s %.1f %s'%(\"Overall efficiency =\",n_overall,\"\")\n",
"\n",
"\n",
"Q=A1*v_r1;\n",
"\n",
"P=n_overall*Q*rho*g*H;\n",
"Ohm_P=w*2.*math.pi/(g*H)**(5/4)*(P/rho)**(1/2);\n",
"\n",
"## sigma > 0.119*(0.5)^(1.84) = 0.0331\n",
"\n",
"sigma=0.0331;\n",
"\n",
"##((p_atm-p_min)/(rho*g)-z0)/H > 0.0331\n",
"\n",
"z0=((p_atm-p_min)/(rho*g))-sigma*H;\n",
"print'%s %.2f %s'%(\"Limiting value for the height of the draft tube above =\",z0,\"m\")\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall efficiency = -1.9 \n",
"Limiting value for the height of the draft tube above = 5.85 m\n"
]
}
],
"prompt_number": 2
}
],
"metadata": {}
}
]
}
|
