Why does squeezing a hose make the water go further?

[Pangolin]

Why does squeezing a hose make the water go futher?

According to the continuity equation, A1v1 = A2v2, reducing the area of the opening will cause the velocity to increase.

However, according to Bernoulli's eqn, increase in velocity will cause a decrease in pressure, so that will mean that the water will be released at lower velocity. In effect, it should cancel out the increase in velocity due to continuity eqn.

Please help me solve this problem. Thank you!

 

[NEWO]

from my understanding a decrease in area of the opening causes an increase in pressure which thus give an increase in velocity. From bernoulli's equation

P_{1}+\frac{1}{2}\rho v_{1}^{2}+\rho gh_{1}=P_{2}+\frac{1}{2}\rho v_{2}^{2}+\rho gh_{2}

where v is the velocity v1 is the velocity in the hose, and v2 is the velocity outside the hose .

 

[Hurkyl]

a decrease in pressure, so that will mean that the water will be released at lower velocity.

Why should that be so?

Why wouldn't water travels as fast as it does when it comes out of the hose precisely because it was traveling that fast inside the hose?

 

[andrevdh]

However, according to Bernoulli's eqn, increase in velocity will cause a decrease in pressure, so that will mean that the water will be released at lower velocity.

Yes, the pressure will decrease in the stream leaving the hose, according to Bernoulli's equation. Just before your thumb the pressure will increase since the speed is lower here in the pipe. This causes a back pressure being transmitted into the water in the pipe (which sometimes causes loose connecions to come undone).

One should fix one's mind on the continuity equation though. Which states the fact that the amount of water flowing past a cross section in a time interval will be the same at any point along the stream. This means that the velocity will increase if the cross section decreases. From this fact we can deduce that the pressure in the high velocity stream need to decrease according to Bernoulli, which we know already from the basics of aerodynamics.

The flow rate will be reduced from an unrestricted pipe to a restricted one though. Test it with a bucket and a stopwatch.