Effect of distance on jet force

[Tom Hardy]

Homework Statement

Apologies for the vague title but I'm not sure how else I could word it, also this isn't really a homework question per se however I'm not too sure where else to ask it.

I think it would help if i set up a scenario. Say there was a pipe that released a fluid to a mass scale underneath the nozzle x meters away and got a reading of 5kg. If the distance between the nozzle and the scale was increased would we expect the reading to change? Assume turbulent flow.

Homework Equations

Mass reading = (density*average flow velocity^2*A)/g

The Attempt at a Solution

I would say no but I'm not sure. If the fluid was incompressible then steady flow would be in effect and the mass would remain constant thus the balance should show the same reading but I feel there's more to it. Once the fluid has left the pipe it no longer feels the driving force of the pump so there's like an acceleration gradient in the jet..wouldn't that mess up the steady flow?

Any help will be appreciated, thank you.

 

[gneill]

Is it possible that by "mass scale" you are intending a weight scale or force or pressure measuring device of some sort)? In other words, something to determine the average force on a surface due to the fluid impacting it?

Is the fluid traveling in a vertical direction under the influence of gravity? If so, consider that the change in height will add kinetic energy and hence momentum to every particle (or differential volume unit) of the fluid as it falls through the gravitational field.

 

[Tom Hardy]

Is it possible that by "mass scale" you are intending a weight scale or force or pressure measuring device of some sort)? In other words, something to determine the average force on a surface due to the fluid impacting it?

Is the fluid traveling in a vertical direction under the influence of gravity? If so, consider that the change in height will add kinetic energy and hence momentum to every particle (or differential volume unit) of the fluid as it falls through the gravitational field.

Yeah that's what I meant. That's an awesome point, can't believe I didn't think of that haha.

Thank you.

 

[NascentOxygen]

I'm trying to picture a high speed jet of water directed downwards from a significant height. The velocity will slow down to a terminal velocity, and I expect the stream will break up into myriad globules. This means it must spread out. So I think it will reach the ground over a wide area as a dense shower like raindrops.

 

[rezeew]

I would approach this question by first understanding the physical principles involved. In this scenario, the force being measured is the jet force, which is the force exerted by the fluid as it exits the nozzle. This force is dependent on several factors, including the density and velocity of the fluid, as well as the area of the nozzle.

Based on the given equation, it appears that the mass reading is directly proportional to the average flow velocity and the area of the nozzle. This means that if the distance between the nozzle and the scale is increased, the average flow velocity would decrease, resulting in a decrease in the mass reading. However, this assumes that the density and area of the nozzle remain constant.

In reality, as the fluid travels a longer distance, it may experience changes in density and velocity due to factors such as friction and turbulence. This could also affect the mass reading. Additionally, the acceleration gradient in the jet may also play a role in altering the flow velocity and therefore the mass reading.

In conclusion, while the mass reading may not change significantly, there are several factors that could potentially affect the jet force as the distance between the nozzle and the scale is increased. Further experiments and calculations would be needed to accurately determine the effect of distance on jet force.