# Finding Speed of Efflux for Two Liquids of Different Densities

• zorro
In summary: I appreciate your help.In summary, the container holds two immiscible non-viscous incompressible liquids of densities d and 2d, each of height H/2. A tiny hole of area S<<A is punched on the vertical side at height h(<H/2). To find the speed of efflux, the pressure difference at the hole is calculated using the density and height of the liquids, and then substituted into the equation for velocity. This approach only provides the initial velocity, as the velocity will change as the level of the liquid decreases and when the liquid with density d begins to flow out.
zorro

## Homework Statement

The container of uniform cross section area A holds two immiscible non-viscous incompressible liquids of densities d and 2d each of height H/2. A tiny hole of area S<<A is punched on the vertical side of the container at height h(<H/2)

Find the speed of efflux.

## The Attempt at a Solution

I know how to find it when there is only one liquid present.
What is the approach in this case?

#### Attachments

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The pressure difference at the hole is
P - Po = g[H/2*d + (H/2-h)*2d ]

The density of the liquid flowing out is 2d. Hence the velocity of the liquid is

v = sqrt[2(P - Po)/2d]

Substitute the values and find v.

Last edited:
rl.bhat said:
The pressure difference at the hole is
P - Po = g(H/2*d + H/4*2d) = gHd

how did you get H/4*2d? the height 'h' is a variable.

rl.bhat said:
The density of the liquid flowing out is 2d

After some time density of liquid flowing out will be d. But we are not taking it into account. Why is it so?

]how did you get H/4*2d?[/B] the height 'h' is a variable.

It should be (H/2 - h)*2d

After some time density of liquid flowing out will be d. But we are not taking it into account. Why is it so?

From the expression we get only the initial velocity. As the level of the liquid decreases, the velocity will also change. When the liquid with density d flows out, again velocity will change.

Thanks alot, Sir.

## 1. What is the purpose of finding the speed of efflux for two liquids of different densities?

The purpose of this experiment is to determine the relationship between the density of a liquid and the speed at which it flows out of a container. This can help us understand the physical properties of different liquids and how they behave under different conditions.

## 2. How is the speed of efflux calculated?

The speed of efflux is calculated by measuring the time it takes for a fixed volume of liquid to flow out of a container, and then using the formula: speed = volume / time. This gives us the average speed of the liquid as it flows out.

## 3. What equipment is needed for this experiment?

To find the speed of efflux for two liquids of different densities, you will need a container with a small hole at the bottom, a stopwatch, a measuring cylinder, and the two liquids with different densities that you want to compare.

## 4. How does the density of a liquid affect its speed of efflux?

The density of a liquid has a direct impact on its speed of efflux. Heavier, more dense liquids will flow out of a container more slowly compared to lighter, less dense liquids. This is because denser liquids have more mass and require more force to flow out of the container.

## 5. What are some potential sources of error in this experiment?

Some potential sources of error in finding the speed of efflux for two liquids of different densities include variations in the size of the hole in the container, inaccurate measurement of the volume of liquid, and human error in timing the flow of the liquid. It is important to take multiple measurements and calculate an average to minimize these errors.

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