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

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Discussion Overview

The discussion revolves around the behavior of flow rate and velocity when the orifice size at the bottom of a water tank is reduced. Participants explore concepts related to fluid dynamics, specifically the conservation of volume flow rate and the effects of pressure differences in different setups.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that reducing the diameter of an orifice should increase the velocity of water flow due to conservation of volume flow rate (A*V is conserved).
  • Others argue that comparing two different setups (connected pipes versus separate tanks) is not valid, as the behavior of the flow may differ significantly between these scenarios.
  • One participant suggests that the pressure difference remains constant when the area of the hole is reduced, which could explain why the velocity does not increase as expected.
  • Another participant points out that upstream of the orifice, the cross-sectional area is larger, leading to lower velocity, while at the orifice, the area is smaller, resulting in higher velocity due to converging streamlines.
  • It is mentioned that flow through a single pipe is conserved, but flow between two different tanks does not have to be equal, as they contain different volumes of water.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the behavior of flow rate and velocity when the orifice size is reduced. Multiple competing views remain regarding the effects of pressure and the validity of comparing different setups.

Contextual Notes

Some assumptions about pressure differences and flow behavior are not fully explored, and the discussion highlights the complexity of fluid dynamics in different configurations.

TheNerdyGuy
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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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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.
 
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)
 
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?
 
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.
 
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
 
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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