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(tap=faucet) When I turn a tap on full and then put my thumb over the spout covering, say, 90% of it, then the water spurts out. If I turn it on to, say 10%, then the water dribbles out.

What's the essential difference between the way that my thumb covers most of the hole and the way the tap valve opens that makes the water come out at a different pressure in either case?

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I like the question, I suspect it has to do with the '10%'. I reckon it takes 99% plus thumb coverage to get the spurt effect. When opening/closing a tap the valve is only in this region for a short time and the effects are hidden inside the tap. –  Nic Nov 4 '11 at 15:32

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up vote 12 down vote accepted

It's the shape of the tap - in fact the very reason for their being a tap rather than just a valve on the end of the pipe.

When you open the valve slightly the water does come out at high speed, hits the inside of the tap spout and is stopped - it then runs out of the tap at slow speed instead of spraying you.

Imagine if you put your finger over the end of the tap to create a spray but then collected that spray in another pipe and looked at the water coming out of the other end of the pipe - it would be a slow trickle, just like the tap.

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The reason is that there is a valve between you and a very high-pressure main pipe. The pressure is not equal across this opening--- it drops to nearly atomospheric pressure, and the water dribbles out at a rate determined by the size. The opening allows a fixed amount of water per unit time through, determined by the pressure drop and Bernoulli's law.

When you cover the opening with your thumb you initially make the water dribble out slower, and the pressure rises closer to that of the main, so it will rise closer to the pressure provided by the water utility. The spray rate is again determined by Bernoulli's law, but now for the much higher pressure in the tap. You can go up all the way to the pressure in the main as you cover more of the opening, and if you cover all the opening, you get the main pressure on your thumb.

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so whats the physical difference between tap valve and thumb valve? –  Nic Nov 4 '11 at 16:24
    
@Nic - There is a pipe around the tap valve to catch the spray. Also, depending on the design, the constriction may be longer, resulting in more drag against the walls. –  Rex Kerr Nov 4 '11 at 16:51
    
Sir, could you explain how tap mechanism obeys Equation of continuity. Does the change of the flow from laminar to cholked cuases ahuge pressure difference. I think if continuity holds then changing the area of opening should not affect the flow rate (i.e $dm/dt$). Sir can you explain some details , i've asked the same question , if you'll explain in your current answer then i will delete my question soon. i saw your profile your answers are very helpful & detailed please add some references in this answer that would be very helpful. –  user31782 Dec 21 '13 at 8:21

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