Estimation and validation of water pressure at nozzle

[Tomtom123]

ρ

I am trying to estimate and validate the pressure of water exiting a nozzle. For an unknown reason, the validation is consistently twice as high as the estimation.

Here the approach:
Estimation:
I am using the dynamic pressure equation for the estimation:
q = 1/2 * ρ * u²

where,
q = dynamic pressure
ρ = density of water (997 kg/m³)
u = liquid velocity
The velocity is calculated based on the known nozzle diameter and the flow rate (u = flow rate / nozzle area)

Validation:
The measurement is performed by simply measuring the jet force with a force gauge in horizontal orientation and in short distance (<1cm) - see the schematic. The assumption is that the jet diameter is the same as the nozzle.
q_val = jet force / nozzle area.

As mentioned before, in varying measurements the validation is close to being twice of the estimation data.
Is there anything I'm missing here?

 

[Chestermiller]

You are not approaching this correctly. Your experimental result is exactly what would be expected. Are you familiar with the Macroscopic Momentum Balance equation?

 

[Tomtom123]

Hi Chestermiller,

Unfortunately, not. Can you please help me understand where my estimation methodology is incorrect?

Thanks

 

[Chestermiller]

Hi Chestermiller,

Unfortunately, not. Can you please help me understand where my estimation methodology is incorrect?

Thanks

You probably have the correct answer for the pressure only at the very center of the jet striking the wall. But the axial flow velocity is not stopped completely over an area equal to the jet coming out of the nozzle. The pressure from the jet hitting the wall is distributed over a much larger area. The way to get the force that the jet exerts on the wall is to perform a momentum balance on the jet. For this system, the macroscopic momentum balance on the jet in the axial direction reduces to $$F=0-\dot{m}v$$where F is the axial force that the wall exerts on the fluid in the positive x direction, $\dot{m}=\rho v A$ is the mass flow rate of the jet, A is its cross section area, and the right hand side of the equation represents the rate of change of axial momentum of the jet. So the force that the wall exerts on the jet is: $$F=-\rho v^2A$$. And the force that the jet exerts on the wall is $+\rho v^2A$. This is twice your stagnation flow estimate, but is consistent with your observed value of the force.