Bernoulli’s Equation and External Forces

[Khalid Qasim]

Summary:: Bernoulli’s Equation and External Forces

Hello all, I am a bit confused on this question:

Water flows through a spray nozzle (as shown in the figure below) at a rate of 50 cm3 h -1 .
The internal inlet diameter of the nozzle entrance is 5 cm and the internal exit diameter of the nozzle is 1 cm.
The gauge pressure is 2.75 bar at the entrance of the nozzle and the pressure outside the nozzle exit is atmospheric.
Calculate the external force required to keep the spray nozzle in place, and the direction of this force.
State any assumptions you make and give all the steps in your calculation.

I have tried using bernoulli's eq to find different velocities to calculate momentums to hopefully find a thrust force, but to no avail. Can someone help?

 

[kuruman]

Please show us what you tried. Then perhaps we can diagnose why "to no avail."

 

[Khalid Qasim]

Please show us what you tried. Then perhaps we can diagnose why "to no avail."

I've crossed it out now, but what I had done:
Found force at the entrance by multiplying 3.76 bar and area at start.
Found force at the exit by multipying 1.01bar and area at exit.

Now for the next part:
Finding the velocities I did: Start: (50x(10^-2)^3)/(3600x(area at start)) = 0.0000708 (which already seems wrong)
Now subbing into bernoullis eq i got the exit velocity as 23.45
so i tried to do a momentum change, but was unsure of the time interval to even use, and I got a bit too confused to continue

 

[kuruman]

What is your strategy for finding the external force required to keep the spray nozzle in place? To guide your thinking, consider two extreme situations in which the pressure at the entrance is 2.75 bar: (a) the exit diameter is plugged and there is no water flow; (b) the exit diameter is the same as the entrance diameter and the fluid flows freely. How would you calculate the required force in each case?

When you respond, please use equations in symbolic form, not numbers and especially not numbers without units attached to them.

 

[Chestermiller]

My first question for you is "Is 2.75 bars at the entrance to the nozzle together with the inlet and exit velocities and the exit pressure of 1 bar consistent with the Bernoulli equation?"

My second question is whether you are familiar with the use of a macroscopic momentum balance to determine the force exerted by the nozzle on the fluid within the nozzle?