Why Does Flow Rate Remain Constant When Reducing Orifice Size in a Water Tank?

In summary, the conversation discusses the principle of conservation of volume flow rate and how reducing the diameter of a hose pipe can increase the velocity of water flow. However, when the area of an orifice at the bottom of a water tank is reduced, the velocity remains the same despite being forced through a smaller hole. This is because the pressure difference and speed are not affected by the reduced area in the second setup. The conversation also mentions that intuition may suggest an increased velocity with reduced area due to increased pressure, but this is not always the case. The difference in behavior between the two setups is attributed to the fact that in one, the same water flows through two parts of a pipe while in the other, different water flows through separate tanks.
  • #1
TheNerdyGuy
8
0
So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Does anyone know why this actually happens?
 
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  • #2
In the first part you consider two connected pipes in a single setup, in the second part you compare two completely different setups. There is no reason why those should behave the same.
 
  • #3
mfb said:
In the first part you consider two connected pipes in a single setup, in the second part you compare two completely different setups. There is no reason why those should behave the same.
Yes but intuitively when area at a point in the tank is reduced then velocity of the water should increase right?(The water is forced to go through a smaller hole)
 
  • #4
TheNerdyGuy said:
Yes but intuitively when area at a point in the tank is reduced then velocity of the water should increase right?
No.
TheNerdyGuy said:
(The water is forced to go through a smaller hole)
It is forced by the same pressure difference, so it gets the same speed.

What happens without a hole?
 
  • #5
In the second case the pressure is not changed by reducing the area of the hole. This is the difference.
Your intuition is based on these situations where reduction of area results in increased pressure. Like squeezing a garden hose.
 
  • #6
TheNerdyGuy said:
Yes but intuitively when area at a point in the tank is reduced then velocity of the water should increase right?(The water is forced to go through a smaller hole)
Far upstream of the hole, the cross sectional area is that of the entire tank, and the velocity is very low. At the oriface, the diameter is much smaller than the tank diameter, and the velocity is much higher. In the region approaching the hole, the streamline pattern is converging, and the effective area for flow is getting smaller as the velocity increases.

Chet
 
  • #7
Flow through a single pipe is conserved, since it's the same water flowing through two parts of the pipe.
Flow through two different tanks doesn't have to be equal between the tanks, since it's not the same water flowing through tank 1 and 2. Obviously, a bigger hole in the bottom of the tank will leak more.
 
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Related to Why Does Flow Rate Remain Constant When Reducing Orifice Size in a Water Tank?

What is the "Flow rate in pipe puzzle"?

The "Flow rate in pipe puzzle" is a problem that involves determining the rate at which a fluid is flowing through a pipe, given certain parameters such as the diameter of the pipe, the length of the pipe, and the pressure difference between the two ends of the pipe.

Why is the "Flow rate in pipe puzzle" important?

The "Flow rate in pipe puzzle" is important in many industries, such as plumbing, chemical engineering, and oil and gas production. Knowing the flow rate of a fluid is crucial for designing efficient systems and ensuring the proper functioning of equipment.

What factors affect the flow rate in a pipe?

The flow rate in a pipe is affected by several factors, including the diameter of the pipe, the length of the pipe, the viscosity of the fluid, and the pressure difference between the two ends of the pipe. Other factors such as the roughness of the pipe's interior surface and any obstructions in the pipe also play a role.

How is the flow rate in a pipe calculated?

The flow rate in a pipe can be calculated using the Bernoulli's equation, which takes into account the pressure difference, fluid density, and the pipe's dimensions. Other equations and models, such as the Darcy-Weisbach equation, can also be used depending on the specific characteristics of the system.

What are the challenges in solving the "Flow rate in pipe puzzle"?

The main challenges in solving the "Flow rate in pipe puzzle" are accurately determining the parameters involved, such as the fluid properties and the pipe dimensions, and selecting the appropriate equation or model to use. Additionally, real-life systems may have unpredictable factors that can affect the flow rate, making it difficult to achieve precise calculations.

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