Pressure increases as density increases.

In summary, as the temperature of water decreases, its density increases and therefore the pressure at the bottom of a container filled with water will also increase. In the second scenario, the pressure at the bottom of a cylinder decreases when the radius is decreased, but remains the same when the height is the same. This is because the pressure is directly proportional to the density and height of the liquid, but inversely proportional to the area of the bottom of the container. Therefore, as long as the density and height are the same, the pressure will be the same regardless of the radius.
  • #1
Physics197
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Homework Statement



Water contracts when cooled (at least above 4 °C). A beaker of water is cooled from 50 °C to 20 °C. The pressure at the bottom of the beaker increases.

Does the pressure increase or decrease as temperature decreases

The absolute pressure at the bottom of a cylinder filled with liquid is Pa=2.0 atm. The liquid is poured into another cylinder having half the radius. The absolute pressure at the bottom of that cylinder is Pa=5.0 atm.

I believe this is false.

Two cylinders are filled with water to the same height, but have different radii. The pressures on the bottoms of the cylinders are the same.

True - radii has no effect, just height?

Homework Equations


The Attempt at a Solution

 
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  • #2


I think your answers are correct. For the first one, you really need a formula to indicate the answer. Do you have a formula for pressure that involves density? Or maybe one without density in it would be even better!
 
  • #3


I do have Pressure = F/Area (surface)
also, Pressure = pgh
 
  • #4


Pressure = ρgh is pretty good.
The cooler water will have a larger ρ, but the water has less volume, so smaller h.
Not very conclusive!

If you multiply by the area of the bottom of the container, and divide by it, you have
Pressure = ρgh = ρAhg/A
Since A*h is the volume, this is P = ρVg/A
Looks just as hopeless, but note that ρV is the mass of the liquid.
Can you finish it off and say what happens to P as the density increases?
 

1. What is fluid pressure?

Fluid pressure is the force exerted by a fluid on an object or surface. It is typically measured in units of force per unit area, such as pounds per square inch (psi) or pascals (Pa).

2. How is fluid pressure calculated?

Fluid pressure can be calculated using the equation P = F/A, where P is pressure, F is force, and A is the area over which the force is applied. In other words, pressure is equal to the force divided by the area.

3. What factors affect fluid pressure?

Several factors can affect fluid pressure, including the density and depth of the fluid, the velocity of the fluid, and the shape and size of the object or surface that the fluid is in contact with.

4. How does fluid pressure change with depth?

Fluid pressure increases with depth due to the weight of the fluid above it. This is known as hydrostatic pressure, and it follows a linear relationship with depth. The greater the depth, the greater the fluid pressure.

5. What is the relationship between fluid pressure and buoyancy?

Fluid pressure and buoyancy are inversely related. As the pressure of a fluid increases, so does its density, which in turn affects the buoyant force it exerts on an object. This is why objects float more easily in lower pressure fluids, such as air, compared to higher pressure fluids, such as water.

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