# What is the difference between high speed water supply and high pressure water supply coming out of a hose?

According to Bernoulli's principle,

$P + \frac{1}{2} d v^2 + dgh = constant$

where, P is pressure, d is density of water, v is velocity and h is height.

Assuming that height of a plastic pipe is kept constant, we get => $P + \frac{1}{2}dv^2 = \text{constant}$.

Now, if we narrow the outlet of the pipe by obstructing the flow of water, both, the speed of the water coming out as well as its pressure increases. For Bernoulli's principle to be true, one has to decrease for the other to increase...

So, how can Bernoulli's principle be correct after this counterexample?

• how do you know the pressure has increased? – danimal Mar 22 '15 at 20:28
• Because if you take a thin tight membrane and aim at it with the end of the pipe narrowed, then the sharper stream of water is more likely to puncture the membrane. Hence, it has more pressure.. – Prem kumar Mar 22 '15 at 20:58
• It's good to note that Bernoulli's equation assumes that no energy is lost to viscosity. That's a pretty poor assumption in pipe flow and discharge through a small opening. – user3823992 Mar 23 '15 at 13:52

## 1 Answer

No,the velocity increases but the pressure decreases. This pressure that you are refering to,is the dynamic pressure,it is the pressure that drives the fluid.That keeps the momentum going. The fluid entering the narrower piece of pipe means that fluid tends to push back the fluid that tries to enter after it.That compresses the micro movements of the tiny particles,thus lowering that dynamic pressure(the micro movements are the causes for pushing the fluid).

• keep in mind that i am not entirely sure about the microscopic analysis that i gave you.Someone might disagree.But the pressure definitely drops. – TheQuantumMan Mar 22 '15 at 20:44
• What about my membrane example- if you take a thin tight membrane and aim at it with the end of the pipe narrowed, then the sharper stream of water is more likely to pucture the membrane. Hence, it has more pressure... – Prem kumar Mar 22 '15 at 20:51
• Also, you wrote- 'This pressure that you are refering to,is the dynamic pressure'. Just in case, I am wondering, is there another kind of pressure other than dynamic pressure... – Prem kumar Mar 22 '15 at 20:53
• There is also static pressure(hydrostatic from the weight of the fluid,but because you said h in constant,so is static pressure).The whole pressure is the sum of the two.What does pucture mean? – TheQuantumMan Mar 22 '15 at 20:56
• Sorry, I meant 'puncture'. – Prem kumar Mar 22 '15 at 20:57