# Pressure - velocity relations for water

• trini
In summary, the conversation discusses the relationship between fluid velocity and pressure, particularly in the context of cleaning surfaces with high pressure pumps. It is explained that in a smaller pipe with higher velocity, there is a decrease in pressure due to conservation of momentum. This explains why high pressure pumps are better at cleaning surfaces than low pressure pumps. The conversation also mentions Bernoulli's equation and the effect of changing area on velocity and pressure. It is concluded that in a high pressure pump, the pressure inside is high while the velocity outside is high, resulting in a low pressure at the nozzle.
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 :)

trini said:
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.

## 1. What is the relationship between pressure and velocity in water?

The relationship between pressure and velocity in water is known as Bernoulli's principle. According to this principle, an increase in the velocity of a fluid will result in a decrease in pressure, and vice versa. This means that when water flows faster, the pressure decreases, and when it flows slower, the pressure increases.

## 2. How does a change in pressure affect the velocity of water?

A change in pressure will cause a corresponding change in the velocity of water, according to Bernoulli's principle. An increase in pressure will result in a decrease in velocity, while a decrease in pressure will result in an increase in velocity. This relationship is important in understanding fluid dynamics and is used in various applications, such as in airplane wings and water pumps.

## 3. What factors can influence the pressure-velocity relationship in water?

Several factors can affect the pressure-velocity relationship in water. These include the shape of the object through which the water is flowing, the density of the water, and the viscosity of the water. Other factors such as the temperature and altitude can also have an impact on this relationship.

## 4. What happens to the pressure and velocity of water in a narrowing pipe?

When water flows through a narrowing pipe, the velocity increases while the pressure decreases. This is because the same amount of water needs to flow through a smaller area, resulting in an increase in velocity to maintain the same flow rate. As a consequence, the pressure decreases in order to balance the forces acting on the water.

## 5. How is the pressure-velocity relationship for water used in engineering and everyday life?

The pressure-velocity relationship for water is used in various engineering applications such as in designing aircraft wings and propellers, water pumps, and hydraulic systems. In everyday life, we can see this relationship in action when we turn on a faucet and the water flows out with a higher velocity due to the decrease in pressure as it moves through the pipes.

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