Velocity of a water jet given water pressure and diameter?

In summary, the conversation is about determining the velocity of a water jet, specifically in the context of a garden hose with a 1/2" diameter and a water pressure of 40psi. The individual is unsure of which equation to use to calculate velocity and suggests considering factors such as time and gallons per minute. Another individual suggests using Newton's second law and provides a formula for estimating flow speed based on size, pressure, and a shape factor.
  • #1
rufnrede
1
0
I need to determine the velocity of a water jet. For example, if a garden hose is 1/2" in diameter and we assume that the water pressure is 40psi, what would be the water velocity (in ft/s) as it exits the hose (assuming no nozzle)?



We know Pressure = force/area, but I want to know the velocity in feet/second, so I don't know what equation to use!



Since velocity has a time component, would we need to introduce another factor? Maybe estimate the gallons per minute? Is this known for a typical garden hose? Thank you in advance!
 
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  • #2
You can estimate flow speed from an orifice given just it's size, the presure and a factor that describes the shape.
Have you tried looking up orifice+flow in your textbook.
 
  • #3
.32 X GPM
_________ = Ft/Sec velocity
TFA (sq. in.)
http://www.uiweb.uidaho.edu/extension/lawn/Files/Garden_Hose.htm [Broken]
 
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  • #4
Use the Newton's second law, considering a small dt amount of time.
 
  • #5


To determine the velocity of a water jet, we can use the Bernoulli's equation, which relates pressure, velocity, and height of a fluid. In this case, we can assume that the height of the water is constant, so we can ignore that term in the equation. Therefore, the equation becomes:

Pressure = (1/2) * density * velocity^2.

Rearranging this equation, we get:

Velocity = √(2 * Pressure/density)

To calculate the density of water, we can use the standard value of 1000 kg/m^3.

Substituting the given values of 40 psi for pressure and 1/2 inch for diameter (which is equivalent to 0.0127 meters), we get:

Velocity = √(2 * 40 psi * 0.0127 m / (1000 kg/m^3))

= √(0.1016 m^2/s^2)

= 0.319 m/s

Converting to feet per second, we get:

Velocity = 0.319 m/s * (3.281 ft/m) = 1.046 ft/s

Therefore, the velocity of the water jet from a garden hose with a 1/2 inch diameter and a pressure of 40 psi would be approximately 1.046 ft/s.

It is important to note that this calculation assumes no friction or losses in the system, so the actual velocity may be slightly lower. Additionally, the velocity may vary depending on the specific garden hose and water pressure used. Estimating the gallons per minute of the garden hose may also help to provide a more accurate calculation.
 

1. What is the formula for calculating the velocity of a water jet?

The formula for calculating the velocity of a water jet is v = √(2P/ρ), where v is the velocity, P is the water pressure, and ρ is the density of water.

2. How does the diameter of the water jet affect its velocity?

The diameter of the water jet does not directly affect its velocity. However, a larger diameter may result in a higher water pressure, which can increase the velocity of the water jet.

3. Can the velocity of a water jet exceed the speed of sound?

No, the velocity of a water jet cannot exceed the speed of sound. The speed of sound in water is approximately 1482 meters per second, which is much higher than the velocity of a typical water jet.

4. How does the shape of the nozzle affect the velocity of the water jet?

The shape of the nozzle can affect the velocity of the water jet by controlling the flow of water. A narrower nozzle can increase the water pressure and therefore increase the velocity of the jet. A wider nozzle can decrease the water pressure and reduce the velocity of the jet.

5. Is the velocity of a water jet affected by the distance it travels?

Yes, the velocity of a water jet can be affected by the distance it travels. As the water jet travels further, it may experience friction and other forces that can decrease its velocity. Additionally, the velocity may decrease as the water jet spreads out and loses pressure over a longer distance.

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