Why flow has high velocity when partially closed?

[nirmaljoshi]

I want to ask why flow has high velocity when partially closed. Eg. when we partially close garden's hose pipe, the flow goes much more farther than when fully open.

Supposing water is flowing through a pipe from a constant level water tank. Why flow has high velocity when partially closed? According to Bernoulli's equation, velocity is given by v^2/2g=h. Thus, velocity should be constant. Isn't it?

 

[Misha Kuznetsov]

I believe it's because the same amount of water has to come out of the hose end per second as goes into the end. Since the gap for it to do so becomes smaller, it is forced to come out at a faster rate (amount of water going through = rate * cross-sectional area). It is the same as if you blow out (through the mouth) when whistling as opposed to when your mouth is fully open.

Please correct me if I got something wrong.

 

[jbriggs444]

If the pressure supplied at the tap were ideal and if the hose itself did not impose any losses then it would not matter how tightly you squeezed your thumb across the end of the hose. The water would squirt at the same speed. That speed could be calculated by equating the pressure energy $pV$ of the water entering the hose to the kinetic energy $\frac{1}{2}mv^2$ of the water squirting out.

In real life, the tap imposes some pressure loss, the hose induces some pressure loss and the plumbing in the house may induce some as well. The pressure at the end of the hose is less than the pressure the water company supplies to your house and the speed of the squirting water is reduced accordingly. But if you press your thumb tightly over the end of the hose, you decrease the flow rate (volume per unit time) going through the hose. This means that those losses become less important. The water under your thumb can reach the full water company pressure and the squirting water can reach full speed as calculated by the equation above.

 

[nirmaljoshi]

If the pressure supplied at the tap were ideal and if the hose itself did not impose any losses then it would not matter how tightly you squeezed your thumb across the end of the hose. The water would squirt at the same speed. That speed could be calculated by equating the pressure energy $pV$ of the water entering the hose to the kinetic energy $\frac{1}{2}mv^2$ of the water squirting out.

In real life, the tap imposes some pressure loss, the hose induces some pressure loss and the plumbing in the house may induce some as well. The pressure at the end of the hose is less than the pressure the water company supplies to your house and the speed of the squirting water is reduced accordingly. But if you press your thumb tightly over the end of the hose, you decrease the flow rate (volume per unit time) going through the hose. This means that those losses become less important. The water under your thumb can reach the full water company pressure and the squirting water can reach full speed as calculated by the equation above.

The loss in hose pipe should insignificant (less than 1%) and it depends on velocity of flow in pipe. Therefore, it is not the loss that should be main variable.

Again if we think flow rate in pipe should be constant as Misha Kuznetsov thinks. Is there any equation to support his idea?

 

[jbriggs444]

The loss in hose pipe should insignificant (less than 1%) and it depends on velocity of flow in pipe. Therefore, it is not the loss that should be main variable.

There is no reason to think that the flow rate in the pipe will be constant!

 

[russ_watters]

The loss in hose pipe should insignificant (less than 1%)...

For an open hose, that's nowhere close to correct. The loss is in excess of 90%.

...and it depends on velocity of flow in pipe.

Yes: so when you restrict the outlet and reduce the flow rate, the velocity through the rest of the pipe except the outlet itself goes down.

Again if we think flow rate in pipe should be constant...

The flow rate is most certainly not constant. What do you think valves are for?

 

[boneh3ad]

For a pretty extensive discussion on this topic, see this thread: https://www.physicsforums.com/threa...d-same-pressure-as-slower-wider-fluid.816605/

At one point in there I actually go through the whole bit of math and show the flow rate through and pressure losses in a garden hose as a function of how much of it you cover with your hand.

In essence, the water speeds up because you have some roughly constant mass flow rate and when you cover the end partially, the same mass has to pass through a smaller area in the same amount of time, thus a higher velocity. As it also turns out, the pressure losses are quite small until you have a fairly large portion of the end covered. Take a look to see the whole discussion. The part where I work out the whole problem is near the end.