Speed of water leaving trough

  • Thread starter European Sens
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In summary, the problem is asking for the speed of water leaving a hole in a rusty water trough, given that the top of the trough is open to the atmosphere and the hole is 0.14 m below the water level. Using Bernoulli's equation, the pressure, density, and acceleration terms can be cancelled out, leaving only the velocity term. However, the velocity at the top of the trough is zero, so the remaining term must be calculated at both the top and the hole in order to find the speed of the water leaving the hole.
  • #1
**Below is the question. No need to solve it for me. Providing me with an equation would be fine. Thanks**

A dairy farmer notices that a circular water trough near the barn has become rusty and now has a hole near the base. The hole is 0.14 m below the level of the water that is in the tank.

The acceleration of gravity is 9.81 m/s^2.

If the top of the trough is open to the atmosphere, what is the speed of the water as it leaves the hole?

Assume that the trough is large enough that the velocity of the water at the top is zero. Answer in units of m/s.
 
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  • #2
Try Bernoulli.
 
  • #3
So...

pressure + 1/2 * density * velocity^2 + density * acceleration * elevation = constant


I believe that density crosses out.

One question is what is the pressure equal to?
 
  • #4
ok i think its 100,000 Pascals. When I plug everything in I get 447.2

Somehow that doesn't seem correct though
 
  • #5
You need to compare a point at the water surface to one at the hole. Both are open to the atmosphere.
 
  • #6
Doc Al said:
You need to compare a point at the water surface to one at the hole. Both are open to the atmosphere.

Could you explain this further?
 
  • #7
Could someone possibly walk me through this. Sound a little more difficult than I'm used to.
 
  • #8
Hi European Sens,

Bernoulli's equation indicates that

[tex]
P + \frac{1}{2} \rho v^2 + \rho g h
[/tex]

is constant along a flow. So the first step is to compute that quantity for the top of the trough, and then separately compute it at the hole. What do you get for those two quantities? Since the quantity is constant, what would you do next?
 

1. What factors affect the speed of water leaving a trough?

The speed of water leaving a trough is affected by the slope of the trough, the volume of water in the trough, the width of the trough, and the height of the water level in the trough.

2. How does the shape of the trough impact the speed of water leaving it?

The shape of the trough can impact the speed of water leaving it by creating different levels of resistance and turbulence, which can affect the flow and speed of the water.

3. Does the type of material the trough is made of affect the speed of water leaving it?

Yes, the type of material can affect the speed of water leaving the trough. For example, a rougher material may cause more resistance and slow down the flow of water.

4. Can the temperature of the water affect the speed at which it leaves the trough?

Yes, the temperature of the water can affect the speed at which it leaves the trough. Warmer water is less dense and therefore flows faster than colder water.

5. How can the speed of water leaving a trough be measured?

The speed of water leaving a trough can be measured using various methods such as using a flowmeter, timing the water with a stopwatch, or using a pitot tube to measure the velocity of the water.

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