Problem on steady flow energy?

Question

a) a pump is is used to move water through a short pipe of diametre 100 mm. The water has a temperature of 15 ͦ C and a pressure of 100kpa. The pump moves the water up a vertical distance of 2m and the water exits to atmospheric pressure. Assume the process is adiabatic and frictionless. If the mass flow rate of the water is required to be 3kg/s, calculate the power required by the pump.

b)how would introduce the effects of friction into the problem described?

Any help would be most appreciated
Thanks!

Answer 1

Apply the Hazen-Williams f(x) - in terms of pressure loss. Then you can just add the equivalent height to the length of pipe to get the Total Dynamic Head = pressure head + friction head + velocity head.

Good luck.

Answer 2

part a is simple.

To first order, the pressure will move the water up part of the way up the pipe. From there to the top requires the addition of energy. The amount of energy is a function of the mass and the height - nothing more.

To second order, you fudge a little. In order to get the desired mass flow through the specified diameter, you have to have a certain velocity. This velocity entails kinetic energy (as well as the potential energy) which the pump has to supply.

Part b is trickier. There are equations for this sort of thing, but they are all approximations. But basically, you have to add the energy required to overcome the friction:

http://www.efunda.com/formulae/fluids/calc_pipe_friction.cfm
http://en.wikipedia.org/wiki/Hazen-Williams_equation

Note that the Hazen-Williams equation is in terms of pressure loss. That means you can just add the equivalent height to the length of pipe to get the "Total Dynamic Head"
(i.e. pressure head + friction head + velocity head)