Calculating Water Speed & Volume from Pressure

In summary, the conversation is about figuring out the speed and volume of water in a town's wells based on the information that each well can shoot a stream of water 8" diameter 12.6m up. The suggestion is to use energy conservation to find the speed, which is calculated to be 15.7 m/s.
  • #1
Physics is Phun
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Maybe this should be in the math section, I'm not sure. I have this friend that works in the water industry that tells me my town runs off of 3 wells that each have the pressure to shoot a stream of water 8" diameter 12.6m up. I was wondering from this information how I could figure out how fast that water must be moving and in turn the volume. So how could I go about doing this?
 
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anyone?
 
  • #3
You can use energy conservation to solve that.
Take the potential energy as 0 at the output of the well.

The energy of the stream at the output of the well is

[tex]\frac{Mv^2}{2}[/tex]​

(no potential energy, only kinetic energy, speed is v, M is the mass of a piece of water)

The energy of the stream at the highest reach, when the velocity drops to zero is:

[tex]Mg[/tex]​

(no kinetic energy, only potential energy)

Since energy is conserved during the motion (without air friction), we have:

[tex]\frac{Mv^2}{2}=Mgh[/tex]​
(h is the highest reach)

We get easily:

[tex]\frac{v^2}{2}=gh[/tex]​
[tex]v={(2gh)}^{1/2}[/tex]​

Finally, this gives v = 15.7 m/s .
 

FAQ: Calculating Water Speed & Volume from Pressure

What is the formula for calculating water speed?

The formula for calculating water speed is v = √(2gh), where v is the water speed in meters per second, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the water column in meters.

How do you calculate water volume from pressure?

To calculate water volume from pressure, you can use the formula V = P/ρg, where V is the volume in cubic meters, P is the pressure in pascals, ρ is the density of water (1000 kg/m³), and g is the acceleration due to gravity (9.8 m/s²).

What units are typically used for measuring water pressure?

Water pressure is typically measured in pascals (Pa) or pounds per square inch (psi). In some cases, it may also be measured in bar or atmospheres (atm).

How does temperature affect water pressure?

Temperature can affect water pressure because as the temperature increases, the volume of water also increases, causing an increase in pressure. This is known as thermal expansion. However, this effect is minimal and usually only noticeable in extreme temperature changes or in large bodies of water.

Is there a simple way to convert pressure into a different unit?

Yes, there are conversion calculators available online that allow you to easily convert pressure from one unit to another. However, it is important to note that these conversions are approximate and may not be completely accurate due to differences in measurement systems.

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