Velocity of Efflux: Dependence on Orifice Size, Height, Gravity, Density

In summary, the velocity of efflux of a liquid through an orifice in the bottom of a tank is not dependent on the size of the orifice, height of the liquid, acceleration due to gravity, or density of the liquid. This can be shown through Bernoulli's equation at the free surface of the fluid and at the exit point of the fluid. However, if the fluid is incompressible, the density will not vary for large heights of the liquid. Additionally, while the velocity will be the same for both very small and very large orifices, the time it takes for the tank to empty will differ.
  • #1
cheapstrike
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Homework Statement



The velocity of efflux of a liquid through an orifice in the bottom of the tank does not depend upon:

A. Size of orifice
B. Height of the liquid
C. Acceleration due to gravity
D. Density of the liquid

Homework Equations

The Attempt at a Solution


My textbook says that Vefflux=√2gH.
The answer given is size of orifice.
How is it dependent on density? Also, if I take a very very small orifice and then a very large orifice, will the velocity be same?
Does density vary for large H?
 
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  • #2
cheapstrike said:
How is it dependent on density?
There is no claim that the speed of efflux is dependent upon the density. Read the question. It asks to pick the variable on which the speed does not depend.
cheapstrike said:
Also, if I take a very very small orifice and then a very large orifice, will the velocity be same?
Yes, but the time it will take for the tank to empty will not.
cheapstrike said:
Does density vary for large H?
If the fluid is incompressible, no.
I suggest that you write down Bernoulli's equation at the free surface of the fluid and at the exit point of the fluid and see what you get.
 
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1. What does "velocity of efflux" mean?

The velocity of efflux refers to the speed at which a fluid (such as a gas or liquid) exits an orifice or opening. It is affected by various factors including the size of the orifice, the height of the fluid above the orifice, gravity, and the density of the fluid.

2. How does the size of the orifice affect the velocity of efflux?

The size of the orifice has a direct impact on the velocity of efflux. Generally, a larger orifice will result in a higher velocity of efflux, as there is more space for the fluid to escape from. This is because a larger orifice allows for a greater volume of fluid to pass through in a given amount of time.

3. Does the height of the fluid above the orifice affect the velocity of efflux?

Yes, the height of the fluid above the orifice does affect the velocity of efflux. The higher the fluid is, the greater the gravitational potential energy it has. This energy is converted into kinetic energy as the fluid flows out of the orifice, resulting in a higher velocity of efflux.

4. How does gravity affect the velocity of efflux?

Gravity plays a significant role in the velocity of efflux. The force of gravity pulls the fluid down towards the ground, increasing its velocity as it flows out of the orifice. However, if the fluid is flowing horizontally, the effect of gravity on the velocity of efflux will be minimal.

5. How does the density of the fluid affect the velocity of efflux?

The density of the fluid also has a noticeable impact on the velocity of efflux. A denser fluid will have more mass and therefore more momentum, resulting in a higher velocity as it exits the orifice. This is why gases, which are less dense than liquids, tend to have higher velocities of efflux.

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