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Does the speed of the water flowing radially outwards from a water jet impacting a sink depend on how far the tap is opened?

At the moment, I understand that the maximum velocity of the water in the vertical jet is constant regardless of how far the tap is open (as it is accelerated by gravity, and disregarding air-resistance), but the volume flow rate is greater the further the tap is opened.

I'm thinking that a higher volume flow rate results in a greater depth around the bottom of the jet which reduces the effect of friction between the water and the sink as the contact surface of the water has reduced, which would decelerate the water at a lower rate than if it were shallower, but am not sure.

Could someone explain precisely how opening a tap affects the radial speed of the water around the bottom of the jet?

EDIT

I should have clarified that, for my question, the area is variable. What I had in mind was more like a variably sized circular hole beneath a constant-height water tank. I used the word "tap" for simplicity, but I realise now this is a bad substitute, and has caused more confusion than intended.

MadCommy
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1 Answers1

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The speed at which water leaves the tap is not constant, as it has a finite area, which remains roughly constant, so increased flow does indeed increase the velocity. ($\dot m= \rho\, VA$)

However, we can still ask the question of how the flow profile of water flowing outward from a jet is dependant on flow rate when jet velocity is held constant.

First let's calculate the reynolds number:

$$Re=\frac{\rho V D}{\mu} \approx \frac{1000\frac{kg}{m^3}\,2\frac{m}{s}1\,cm}{900 Pa\,\mu s}\approx 20000$$

So the viscous effects are going to be tiny during the transition, which means we can use bernoulli's equation. The pressure will be at atmospheric, before and after the transition, and the height will be the same, so the velocity will be the same.

In conclusion, the spray will just get thicker, but remain at the same velocity when the flow rate is increased. Of course, far from the jet the viscous effects will begin to matter more as the fan thickness decreases, and the reynolds number drops. Then indeed the thicker flow will remain at high speed for longer.

Eph
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