Calculating required pump pressure to maintain flowrate in a uniform horizontal pipe

[Dave-RR]

Homework Statement

I am having trouble with calculating the required pump pressure in a horizontal water pipe, 3Km long. i know that the flowrate is 600Kg/s, average velocity 5.6m/s, cross-sectional area of pipe is 0.107143m^2 and losses due to friction average 0.002 per meter

Homework Equations

pressure=force/area
bernoulli's equation

The Attempt at a Solution

pressure = (flowrate x G)/cross-sectional area
= (600 x 9.81) / 0.107143 = 54935.92 Pa

i think that this is the pressure at the end of the pipe however i am unsure how to caculate the pump pressure given the frictional loss coefficient. i have had very little teaching in fluid mechanics but have researched Bernoulli's equation however i cannot see how it, is applicable to this problem is there any other equations i could use given the known elements

 

[zeebek]

Reynolds number is about

$$\frac{U D}{\nu} = 1.7 \times 10^6$$

This is clearly turbulent and not potential. Bernoulli's equation is not applicable here.

The solution is based on the exact statement, that for a steady flow in pipes mean pressure gradient is balanced by the shear at the wall. IF you work it out in spherical coordinates and by "friction" you mean Darcy friction factor, then

$$\Delta P = f \rho U^2 L / D /8 = 0.002 * 5.6^2 * 3000 / 0.3 / 8 \approx 80 \, Pa$$