What is the diameter of the hole for a flow rate of 4.17x10-5 m3/s?

In summary, a tank filled with water and open to the atmosphere has a small hole 15 m below the water level with a flow rate of 4.17x10-5 m3/s. To find the diameter of the hole, Bernoulli's theorem can be used to calculate the velocity of the liquid flowing out of the hole, which can then be used to determine the area of the hole.
  • #1
Alu
5
0

Homework Statement


A large tank is filled with water and open to the atmosphere has a small hole in its side at a point 15 m below the water level. If the rate of flow from the hole is 4.17x10-5 m 3/s .
What is the diameter off the hole (in mm)

Homework Equations


R=A*V, where R is the rate flow
 
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  • #2


In side the tank at the depth h the total pressure = Pa + ρgh. Velocity of the the liquid is zero.
Out side the hole the pressure = Pa.
Using Bernoulli theorem find the velocity of liquid flowing out of the hole, From that find the area of the hole.
 
  • #3
, A is the cross-sectional area, and V is the velocity

The diameter of the hole can be calculated using the formula d = 2 * √(R/π*V), where d is the diameter, R is the rate of flow, and V is the velocity.

The Solution

To find the diameter of the hole, we need to first calculate the velocity of the water flowing out of the hole. We can do this by rearranging the equation R=A*V to V=R/A.

Substituting the given values, we get V = (4.17x10-5 m3/s) / (π*(15 m)2) = 1.85x10-7 m/s.

Now, we can plug this value into the formula d = 2 * √(R/π*V) to find the diameter of the hole.

d = 2 * √(4.17x10-5 m3/s / π * 1.85x10-7 m/s) = 0.0052 m or 5.2 mm.

Therefore, the diameter of the hole is approximately 5.2 mm.
 

What is flow through a hole?

Flow through a hole refers to the movement of fluid, such as water or air, through an opening or orifice. This can occur in various scenarios, such as when liquid is poured through a small hole or when air is forced through a tiny opening.

How is the flow rate through a hole determined?

The flow rate through a hole is determined by several factors, including the size and shape of the hole, the pressure difference between the two sides of the hole, and the properties of the fluid. These factors can be mathematically calculated using equations such as Bernoulli's principle and the continuity equation.

What is the relationship between the size of the hole and the flow rate?

The size of the hole has a direct impact on the flow rate through it. Generally, a larger hole will allow for a higher flow rate, as there is more space for the fluid to move through. However, other factors such as pressure and viscosity can also affect the flow rate.

How does the shape of the hole affect the flow rate?

The shape of the hole can also impact the flow rate. For example, a round hole will typically allow for a smoother and more efficient flow compared to a square or irregularly shaped hole. This is because round holes have a more even distribution of pressure around the edges, while square or irregular shapes can create turbulence and resistance.

What are some real-world applications of flow through a hole?

Flow through a hole has many practical applications, such as in plumbing systems, where water flows through pipes and faucets. It is also important in industries such as aerospace, where air flows through small openings in aircraft engines. Understanding flow through a hole is crucial in designing and optimizing these systems for efficient and safe operation.

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