# Pressure - velocity relations for water

• trini

#### trini

Ok, so I've been getting confused about some things recently. I've read that fluid flowing in a pipe at higher velocity has less pressure than one flowing slowly. So this means that the less pressure the fluid has, the more momentum it has as it has greater velocity.

So suppose I were trying to clean a surface with a high pressure washer, i know from experience that the water hits the ground harder than if i just used a hose by itself. Now, if i have a pump at high pressure, it means that it should have low velocity right? why is it then that high pressure pumps are better at cleaning surfaces than low pressure pumps if the water should have less impact.

Also, if i had a water flowing from a bigger pipe to a smaller pipe, i would have a velocity increase by conservation of momentum and so get a pressure drop right? so does this mean that the water coming out of a small pipe, even though it has less pressure, would be better for cleaning than the larger higher pressure pipe?

The effect of change in velocity on the pressure can be shown mathematically.
lets assume that a liquid is flowing from a pipe of area A1 with velocity V1. The pipe is connected to another one with a smaller area A2 and the velocity now will become V2 (which will be greater than V1 as per equation 2). We now have two equations:

1) P1 + 1/2(∂V12) = P2 + 1/2(∂V22) ... (Bernoulli's equation) ( where ∂ is density of water)

2) A1V1 = A2V2 ... (equation of continuity)
After solving these 2 equations we get:

P1 - P2 = 1/2 ∂( A12/A22 - 1)V12
Since A1 is larger than A2, the quantity on right is positive and P2 must be less than P1.
What happens in a hose is that the area of nozzle is less which increases velocity of water and decreases the pressure. In these cases we are observing the effect of change of area on change in velocity and pressure.
In a high pressure pump the pressure inside pump is very high compared to outside. Which means that velocity inside the pump is less as compared to what you get outside. So using a high pressure pump will give you "low" velocity "inside" but will give you "high" velocity "outside".

hmm so its kind of like a circuit then, with the pump being the supply? and then this should mean that the pressure at the nozzle itself is quite low yes?

I'm no expert on this, but the following makes sense to me:

Imagine a big syringe with a tiny nozzle, filled with water. Now push the water using as much force as you can apply. The water inside the syringe is now under high pressure due to the tiny nozzle. Since relatively little volume of water escapes through the nozzle, the the piston, and thus water inside the syringe, will move at a very low speed.

At and beyond the nozzle, there are essentially no forces trying to push the water back into the syringe, so the pressure drops dramatically.

Of course, I could be wrong :)

hmm so its kind of like a circuit then, with the pump being the supply? and then this should mean that the pressure at the nozzle itself is quite low yes?

yes, the pressure will be low inside the nozzle as compared to the pressure inside the pump.