Air flow pipe size reduction|Incompressible&Lossless COMPLETED ANSWER

[DylanW]

Homework Statement

Q4. A horizontal air duct reduces from 0.75 m2
to 0.20 m2
.
a) Assuming no losses and an incompressible fluid, what pressure change will occur when 6 kg/s
of air flows through the duct? Use a density of 3.2 kg/m3
for these conditions.
b) Is the incompressible assumption justified?
c) If the jet exits the smaller pipe and strikes a vertical wall, what force will it transmit?

Homework Equations

MassFlowRate = rho.V.A
Bernoullis

The Attempt at a Solution

rho(A).Velocity(A).Area(A)=mass flowate therefore Velocity(A) = 2.5
Mass Flow Rate is Constant
rho(A).Velocity(A).Area(A)=rho(B).Velocity(B).Area(B) therefore Velocity(B) = 9.375
Bernoullis - can't be bothered typing original equation will just type final rearrangement
Pressure(A) - Pressure(B) = [(Velocity(B)^2 - Velocity(A)^2)Rho]/2 which equals 130.625 Pascals pressure difference. Seems a bit low?

For part b, is the incompressible assumption justified? I don't think that it is, because it's density it is a gas and would definitely compress which may explain the results from part A?

For Part C) I'm not so sure of this, I think it would be the Absolute pressure over the area of the Jet so (x Pascals / 0.2 m^2) but I am not sure how to find the absolute pressure, only the difference. Thanks :D

 

[DylanW]

For Part C, I've used the equation P(Dynamic) = [rho.V^2]/2 giving a dynamic pressure of 140.625 Pa and verifying my answer from part 1. Then Using P=F/A -> F = PA I've calculated a force of 28.125N. I am worried that I am ignoring static pressure but I can't see any other way with the information provided.