How Do You Calculate the Flow Rate from a Rectangular Opening in a Tank?

In summary, the conversation discusses how to determine the volume of water that emerges from a rectangular opening in the side of a large water tank. The opening has a given width and height, and the goal is to find the volume of water that emerges per second. The use of Bernoulli's equation and integration are suggested as possible methods to solve this problem. The question of finding the velocity at an arbitrary depth is also raised.
  • #1
burningnachos
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Homework Statement



A rectangular opening is cut into the side of a large open-topped water tank. The opening has width W and height H2 - H1, where H1 is the distance from the top of the tank to the top of the opening, and H2 is the distance from the top of the tank to the bottom of the opening. Determine the volume V of water that emerges from the opening per second.

You may assume that the surface area of the tank is extremely large compared to the area of the opening, but you should not assume that the water emerges from the opening with a single, uniform velocity.

Homework Equations



Bernoulli's equation

The Attempt at a Solution



So I first tried to get the velocity at H1 and H2 using Bernoulli's equation. Then I assume you have to integrate to account for the rate in between, but I'm having trouble setting up the integral. Help is appreciated, thanks.
 
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  • #2
Can you find the velocity at any arbitrary depth y?
 

FAQ: How Do You Calculate the Flow Rate from a Rectangular Opening in a Tank?

What is the flow rate from a hole in a tank?

The flow rate from a hole in a tank is the volume of fluid that passes through the hole per unit time. It is usually measured in liters per second or cubic meters per hour.

How is the flow rate from a hole in a tank calculated?

The flow rate from a hole in a tank can be calculated using the equation Q = A * v, where Q is the flow rate, A is the area of the hole, and v is the velocity of the fluid passing through the hole.

What factors affect the flow rate from a hole in a tank?

The flow rate from a hole in a tank can be affected by several factors, including the size and shape of the hole, the pressure of the fluid, the viscosity of the fluid, and the height of the fluid above the hole.

Why is it important to know the flow rate from a hole in a tank?

Knowing the flow rate from a hole in a tank is important for many reasons. It can help in designing efficient drainage systems, determining the rate of leakage in a tank, and understanding the behavior of fluids in different situations.

How can the flow rate from a hole in a tank be controlled?

The flow rate from a hole in a tank can be controlled by adjusting the size of the hole, changing the pressure of the fluid, or using valves or other devices to regulate the flow. Additionally, the flow rate can also be controlled by changing the properties of the fluid, such as its viscosity.

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