# Question dealing with density and pressure

• tophat22
In summary, pressure varies depending on altitude, and you would need to integrate to find the force on the dam at different depths.
tophat22
I haven't taken physics in a while, and most of this is physics related. My professor's lectures have not helped me understand the material, so I have questions on my homework. I would like to learn how to approach this problem and solve it.

The figure shows a vertical dam holding back a reservoir of depth h. The lower half of the reservoir consists of a sludge whose density is twice that of water, and the upper half of the reservoir's volume consists of pure water.

a. Determine how pressure depends on altitude z in the water and sludge.
b. Let w be the dam's width, and determine the horizontal component of force on the dam.

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Welcome to PF!

Hi tophat22! Welcome to PF!
tophat22 said:
The figure shows a vertical dam holding back a reservoir of depth h. The lower half of the reservoir consists of a sludge whose density is twice that of water, and the upper half of the reservoir's volume consists of pure water.

a. Determine how pressure depends on altitude z in the water and sludge.
b. Let w be the dam's width, and determine the horizontal component of force on the dam.

a. The pressure is basically the weight of the fluid above (per area).

b. Pressure = force per area, so the force on the dam is the integral of pressure times area.

for part a, what am I supposed to do with vector z? will I have to deal with an integral?

Hi tophat22!
tophat22 said:
for part a, what am I supposed to do with vector z? will I have to deal with an integral?

No, you'd only need an integral if the density was varying continuously

but here, it's constant to a certain height, and then a different constant, so you can just multiply instead of integrating.

tiny-tim said:
Hi tophat22!

No, you'd only need an integral if the density was varying continuously

but here, it's constant to a certain height, and then a different constant, so you can just multiply instead of integrating.

Since the pressure varies with depth there will be a different force on the dam at different depths. So integration would be needed.

CS

tophat22 said:
for part a, what am I supposed to do with vector z? will I have to deal with an integral?
stewartcs said:
Since the pressure varies with depth there will be a different force on the dam at different depths. So integration would be needed.

CS

Hi stewartcs!

Not for part a.

tiny-tim said:
Hi stewartcs!

Not for part a.

Sorry I missed the "part a" there! Silly me...I should not post until my morning tea!

CS

It's afternoon here in London!

'll soon be proper tea-time

… and time for "Countdown" on telly.

## 1. What is the relationship between density and pressure?

Density and pressure have an inverse relationship. This means that as density increases, pressure decreases, and vice versa. This relationship is described by the formula pressure = density x gravitational constant x height.

## 2. How does temperature affect density and pressure?

As temperature increases, density decreases, which results in a decrease in pressure. This is because as temperature increases, the particles in a substance gain more energy and move farther apart, making the substance less dense. This decrease in density leads to a decrease in pressure.

## 3. What is the difference between density and specific gravity?

Density is the measure of how much mass is contained in a given volume of a substance, while specific gravity is the ratio of the density of a substance to the density of a reference substance, usually water. In other words, specific gravity is a unitless number that compares the density of a substance to the density of water.

## 4. How does altitude affect density and pressure?

As altitude increases, both density and pressure decrease. This is because as altitude increases, the air becomes less compressed and therefore less dense. The decrease in density leads to a decrease in pressure, as there are fewer particles pushing against a given area.

## 5. How is density and pressure used in weather forecasting?

Density and pressure play a crucial role in weather forecasting. Changes in pressure can indicate the movement of air, which can help forecasters predict the direction and strength of weather systems. Similarly, changes in air density can also indicate changes in temperature and humidity, which are important factors in determining weather patterns.

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