# Finding the gauge pressure at the bottom of a barrel

• Vanessa Avila
In summary, the problem involves finding the gauge pressure at the bottom of a barrel containing a 0.130-m layer of oil with a density of 610 kg/m3 floating on top of water that is 0.290 m deep. The pressure is calculated by adding the pressures from the oil and the water separately, which are found by multiplying their densities, gravitational acceleration, and respective depths. It is important to note that the depth given is only for the water and not for the entire barrel.
Vanessa Avila

## Homework Statement

A barrel contains 0.130-m layer of oil floating on water that is 0.290 m deep. The density of the oil is 610 kg/m3
What is the gauge pressure at the bottom of the barrel?

P [/B]= ρ(g)(h)

## The Attempt at a Solution

I found the pressure of the oil which is 777 Pa by 610kg/m^3(9.8)(0.130m)
for this one I know I have to add the 777 Pa, but I messed up on the height. I used 0.16 by taking the difference of 0.290m-0.130m = 0.16 m and used that height to multiply to the 1000kg/m^3(9.8)(0.130m)

Can someone explain to me why it's not 0.16m? Does that part of the barrel only take into consideration the pressure of water?

There are two liquids contributing to the pressure at the bottom. You need to calculate the pressure from each separately and then add the two pressures.

Vanessa Avila
Vanessa Avila said:
Can someone explain to me why it's not 0.16m
Because the water isn't 0.16m deep, it's 0.290m deep.

Vanessa Avila
Ohhh! I get it! You thought they said the total depth was 0.29m and you subtracted to get the depth of the water. Reread the problem. The depths of the oil and the water are given separately. 0.29m is the depth of the water alone.

Vanessa Avila
Oh, I see now! Thanks all!

## 1. What is gauge pressure and how is it different from absolute pressure?

Gauge pressure is the pressure measured relative to atmospheric pressure, while absolute pressure is the total pressure, including atmospheric pressure. Gauge pressure is often used for practical applications, such as measuring the pressure inside a container, while absolute pressure is used for scientific calculations.

## 2. How is the gauge pressure affected by the depth of a liquid in a container?

The gauge pressure at the bottom of a container depends on the depth of the liquid above it. The deeper the liquid, the higher the gauge pressure, as the weight of the liquid exerts more force on the bottom of the container.

## 3. What is the formula for calculating the gauge pressure at the bottom of a barrel?

The formula for calculating gauge pressure is P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the depth of the liquid. This formula assumes a constant density and a uniform gravitational field.

## 4. How does the shape of the container affect the gauge pressure at the bottom?

The shape of the container does not affect the gauge pressure at the bottom as long as the depth of the liquid is the same. The only factors that affect gauge pressure are the density of the liquid, the depth of the liquid, and the acceleration due to gravity.

## 5. Can the gauge pressure at the bottom of a container ever be negative?

No, the gauge pressure at the bottom of a container can never be negative. This is because gauge pressure is always measured relative to atmospheric pressure, which is always positive. However, the absolute pressure at the bottom of a container can be negative in certain situations, such as when there is a vacuum inside the container.

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