Calculating mass flow rate while assuming shock losses

[Taylor0304]

Below is a 2 part question regarding gravitational pipe flow, I have managed to do Q1) and have got an answer of 144 kg/s. However Q2 asks that shock losses be considered, Although I know how to calculate the shock pressure loss I am unsure of how to apply this to my calculation to get a new mass flow rate value, an explanation would be great, thanks.

1. Homework Statement

Q1) Water flows through a pipe from one reservoir to a lower reservoir. The difference in height of the water levels in the reservoirs is 1.5m. The pipe is 0.5km long with a constant internal diameter of 400mm. It has a surface roughness of 0.20mm. Determine the mass flow rate of water. You may assume negligible shock losses. You will need to iterate to find a solution.

Q2) Repeat Q1 but allow for shock losses in the pipe. Assume that total shock losses (pipe
inlet, outlet and all pipe connections and valves) are equal to 5 times the velocity pressure
in the pipe.

Homework Equations

Bernoulli equation
Darcy equation

The Attempt at a Solution

I believe the change in pressure is 3270pa but I'm not sure how to apply this to get a new mass flow rate value.

rho/2 x C^2 = 1000/2 x 1.144^2 = 654
654 x 5 = 3270Pa

 

[nilesh_pat]

To answer Q2, you have to calculate the pressure loss due to shock losses and add this to the pressure drop calculated from the Bernoulli equation. The pressure loss due to shock losses can be calculated using the following equation: ΔP = K * (ρV2/2g)where K is the coefficient of discharge for the pipe fittings, ρ is the density of the fluid, V is the average velocity, and g is the acceleration due to gravity. With K = 5, you can calculate the pressure loss due to shock losses. This pressure loss should be added to the pressure drop calculated from the Bernoulli equation, and the new mass flow rate can be calculated using the Darcy equation.