A 16-inch gasoline pipe line is transport gasoline at a flow rate of 200 gallon

Question

A 16-inch gasoline pipe line is transport gasoline at a flow rate of 200 gallon per minute. Please calculate how much pressure gradient dp/dx is needed, using the N-S equation provided in below (Hint: Assuming the flow in the pipe line is laminar so you can use the Poisson flow to solve the problem. Dynamic viscosity of gasoline is 0.0006 N/m*2 second: density of gasoline is 0.77 kg/L.) Cylindrical coordinates (r.6,z): We consider an incompressible , isothermal Newtonian flow (density p-const, viscosity const), with a velocity field V-(u g,i Incompressible continuity equation at eq a) Velocity profil not changing over z: ou oz r-component 0 0z eq b) Xial symetric = 6-component eq c) 1 2-component Ou eq d) Op

Explanation / Answer

Given, Q = 200 gallon/min = 0.0126 m3/sec

d = 16 inch = 0.4064 meter

As per the instructions, we will use the Poisson flow equation to solve the problem.

We know, h = 32µUL/gD2

So dp/dx = 32µU/D2

We know U = Q/A = 0.0126/0.1297 = 0.09714 m/s

dp/dx = (32*0.0006*0.09714)/(0.4064)2

dp/dx = 0.01129

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