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+clc
+clear
+printf("example 4.21 page number 160\n\n")
+
+//to find the pressure gradient
+
+Q=0.0003 //in m3/s
+d=0.05 //in m
+A=(3.14*d^2)/4;
+
+u=Q/A;
+
+density=1000; //in kg/m3
+viscosity=0.001; //in Pa-s
+e=0.3;
+dp=0.00125; //particle diameter in m
+
+Re=(dp*u*density)/(viscosity*(1-e));
+fm=(150/Re)+1.75;
+L=0.5 //in m
+delta_Pf=fm*((density*L*u^2)/dp)*((1-e)/e^3); //in Pa
+
+//applying bernoulli's equation, we get
+delta_P=delta_Pf-(density*9.8*L);
+pressure_gradient=delta_P/(L*1000); //in kPa/m
+printf("required pressure gradient = %f kPa/m of packed height",pressure_gradient)