Determine the speed at which the water leaves the hole

In summary, a large storage tank filled with water develops a hole 15.0 m below the water level, causing a flow rate of 2.10x10-3 m3/min. Using the equation F=eta(Av/d), the speed of the water leaving the hole can be determined to be 17.15m/s. To find the diameter of the hole, the volumetric flow rate equation Q=Av can be used, with the area A being calculated from the given values. Alternatively, the conservation of energy equation can be used, assuming constant velocity across the whole area of the hole.
  • #1
Sunsing
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0

Homework Statement



A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 15.0 m below the water level. If the rate of flow from the leak is 2.10x10-3 m3/min

(a) Determine the speed at which the water leaves the hole. =17.15m/s


(b) Determine the diameter of the hole. = ?


Homework Equations



F=eta(Av/d)

I'm not sure what equation to use for this.

The Attempt at a Solution



I'm just not sure how to start this.
Any suggestions?
 
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  • #2
The volumeteric flow rate is given by Q = Av.

You are given Q and you have apparently found v (the velocity), so just solve for A (the area) and then calculate the diameter.
 
  • #3
a) Conservation of energy. The pressure energy of the water just inside the hole is equal to the kinetic energy of the water just outside the hole. See Bernoulli for terms in the equation.

b) I think it is acceptable (= a good approximation) to assume constant velocity across the whole are of the whole so stewartcs' formula applies.
 

1. What factors affect the speed at which water leaves a hole?

The speed at which water leaves a hole can be affected by several factors, including the size of the hole, the amount of water pressure, the height of the water column, and the viscosity of the water.

2. How can I calculate the speed at which water leaves a hole?

The speed at which water leaves a hole can be calculated using Bernoulli's equation, which takes into account the water pressure and the height of the water column. The equation is v = √(2gh), where v is the speed, g is the acceleration due to gravity, and h is the height of the water column.

3. Does the shape of the hole affect the speed of water leaving?

Yes, the shape of the hole can affect the speed of water leaving. A round or circular hole will produce a more consistent and predictable flow compared to an irregularly-shaped hole, which can cause turbulence and decrease the speed of the water leaving.

4. How does the speed of water leaving a hole change with different types of liquids?

The speed of water leaving a hole can vary depending on the viscosity of the liquid. Thicker liquids, such as honey, will have a slower speed compared to thinner liquids, such as water. Additionally, different liquids have different surface tensions, which can also affect the speed of water leaving a hole.

5. Can the speed of water leaving a hole be controlled?

Yes, the speed of water leaving a hole can be controlled by adjusting the water pressure, the size and shape of the hole, and the height of the water column. Additionally, using a nozzle or valve can help regulate and control the speed of the water leaving the hole.

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