Fluid mechanics formula question

[Abigail1997]

1. Homework Statement
See image.

Homework Equations

I thought that Fx=p*u1*A1(u1+u2)+(p1*a1)+(p2*a2) would be the correct formula however I cannot seem to get the stated answer of 1.8kN.

The Attempt at a Solution

Using the above formula, p1v1=p2v2 to find u2 and p1a1=p2a2 to find p2
Fx=999*3*0.00025*(2*11.58)+((710*0.0025)+(2730.8*0.00065))
gives 105

 

[billy_joule]

Could you show all your working please.
It's a little unclear why our how you think you found P2, you don't need to find it, you're told it's atmospheric which is 0 Pa relative to P1 (presumably 'gate pressure' is a typo for gauge pressure).
Also not sure how you found the outlet velocity, conservation of mass/the continuity equation ( vA = constant) is the standard approach.

 

[Chestermiller]

View attachment 104582 1. Homework Statement
See image.

Homework Equations

I thought that Fx=p*u1*A1(u1+u2)+(p1*a1)+(p2*a2) would be the correct formula however I cannot seem to get the stated answer of 1.8kN.

The Attempt at a Solution

Using the above formula, p1v1=p2v2 to find u2 and p1a1=p2a2 to find p2
Fx=999*3*0.00025*(2*11.58)+((710*0.0025)+(2730.8*0.00065))
gives 105

You have applied the conservation of momentum equation incorrectly. The first and third terms are incorrect.

Including the unit vectors, what are the forces acting on the fluid contained within the control volume?
Including the unit vector, what is the rate of momentum exiting the control volume?
Incuding the unit vector, what is the rate of momentum entering the contol volume?