Find force when given air pressure and volume

This is because the slope of a linear function is constant, so the average value will be the midpoint between the highest and lowest values. The pressure at the water surface is one atmosphere and at the bottom of the dam, it is one atmosphere plus the weight of the water column above it. Therefore, the average pressure is equal to one atmosphere plus half of the weight of the water column. This can be calculated using the formula P = ρgh, where ρ is the density of water (1000 kg/m^3), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the water column (10 m). Plugging in these values, the average pressure is 49000 Pa
  • #1
physics1007
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The vertical surface of a reservoir dam that is in contact with the water is 170 m wide and 10 m high. The air pressure is one atmosphere. Find the magnitude of the total force acting on this surface in a completely filled reservoir. (Hint: The pressure varies linearly with depth, so you must use an average pressure.)

Could anyone please help me with this. Its part of an assignment due. The question comes from "Physics 7th edition by Cutnell" Chapter 11 problem 26.

I know that Pressure=Force/Area but no idea how to solve this problem. I also know the p2=p1+pgh equation but don't know if i need this.:uhh:
 
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  • #2
The hint shows you the way. What's the average pressure? (What's the pressure at the water surface? At the bottom of the dam?)
 
  • #3
OK. Thanks. I got the right answer.
 
Last edited:
  • #4
Since pressure varies linearly with height, the average pressure will be smack in the middle between the two extremes.
 

1. What is the relationship between air pressure and volume?

The relationship between air pressure and volume is described by Boyle's Law, which states that when the temperature is constant, the pressure of a gas is inversely proportional to its volume. This means that as the volume of a gas decreases, its pressure will increase, and vice versa.

2. How do you calculate force from air pressure and volume?

To calculate force from air pressure and volume, you can use the formula F = P x V, where F is the force, P is the air pressure, and V is the volume. This formula is derived from the ideal gas law, which states that pressure and volume are directly proportional to the number of molecules and temperature of a gas.

3. What units are used to measure air pressure and volume?

Air pressure is typically measured in units of pressure, such as pounds per square inch (psi) or pascals (Pa). Volume is usually measured in units of length, such as cubic meters (m3) or liters (L).

4. Can air pressure and volume affect the force of an object?

Yes, air pressure and volume can affect the force of an object. When an object is placed in a gas, the gas molecules will exert a force on the object due to collisions. The greater the air pressure and volume, the more collisions and therefore the greater the force exerted on the object.

5. How can changes in air pressure and volume impact everyday life?

Changes in air pressure and volume can impact everyday life in many ways. For example, changes in air pressure can affect weather patterns, causing storms or creating calm conditions. Changes in air volume can also impact the performance of engines and machines, as well as the health and safety of living organisms.

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