- #1

ussername

- 60

- 2

## Homework Statement

(question one is irrelevant for my problem).

What is the pumping power? From energy balance I got a negative value - but it should be positive since the mechanical work from pump is given into system.

## Homework Equations

The input+output velocity:

$$v=\frac{\dot{V}}{A}$$

The friction coefficient:

$$f=\frac{\left |\Delta p \right |}{\frac{L}{D}\frac{1}{2}\rho v^{2}}$$

Moody diagram (not shown here).

The energy balance of open system:

$$\dot{W}=\dot{m}\cdot \left (h_{out}-h_{in}+\frac{v^{2}_{out}-v^{2}_{in}}{2}+g\cdot (z_{out}-z_{in}) \right )$$

The specific enthalpy:

$$h=u+\frac{p}{\rho }$$

## The Attempt at a Solution

The velocity of input and output is ##v=5\,m\cdot s^{-1}##.

From calculated Reynolds number and relative roughness I found friction coefficient ##f=0.02## in Moody diagram (that is a correct value).

The pressure loss due to friction was calculated from the given equation: ##p_{F,out}-p_{F,in}=-5MPa##.

The hydrostatic pressure loss is ##p_{H,out}-p_{H,in}=\rho \cdot g\cdot (z_{out}-z_{in})=-177kPa##.

The total pressure loss is ##p_{out}-p_{in}=p_{F,out}-p_{F,in}+p_{H,out}-p_{H,in}=-5000000-177000=-5177kPa##.

The enthalpy change between outlet and inlet is:

##h_{out}-h_{in}=\frac{p_{out}-p_{in}}{\rho }=\frac{-5177000}{1000}=-5177\,J\cdot kg^{-1}##.

The change of potential energy between outlet and inlet is:

##e_{p,out}-e_{p,in}=g\cdot (z_{out}-z_{in})=9.81\cdot 18=174.58\, J\cdot kg^{-1}##

The resulting power of the pump is:

##\dot{W}=1000\cdot 1\cdot (-5177+174.58)=-5MW##