Question on pressure, volume and rates of change

In summary, a large tank of water with a connected hose has a compressed air between the water surface and the top. When the water height is 3.5m, the absolute pressure of the compressed air is 4.20*10^5Pa. Assuming constant temperature, the speed of the water flowing out of the hose at 3m and 2m is determined using the ideal gas equation and Bernoulli's principle. To find the height at which the water stops flowing, the pressure at that height must be equal to atmospheric pressure.
  • #1
coding_delight
3
0

Homework Statement


A large tank of water has a hose conected to. The tank (a cylinder) is 4.0 m in height and the tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the value 3.50m, the absolute pressure p of the compressed air is 4.20*10^5Pa. Assume that the air above the water expands at constant temp. and take the atmospheric pressure to be 1.00*10^5Pa. What is the speed at which the water flows out of the hose at h = 3.0m and h = 2.0m? at what value h does the water stop flowing?


Homework Equations



I'm pretty sure this involves the ideal gas equation of state PV = nrT and maybe the fact that the volume increase or decrease dV with respect to time is equal to the height increase or decrease dh with respect to time...

The Attempt at a Solution



I have tried quite a few things but to be honest I am stumped at how to approach this problem so please help...i strongly appreciate it...
 
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  • #2
coding_delight said:

Homework Statement


A large tank of water has a hose conected to. The tank (a cylinder) is 4.0 m in height and the tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the value 3.50m, the absolute pressure p of the compressed air is 4.20*10^5Pa. Assume that the air above the water expands at constant temp. and take the atmospheric pressure to be 1.00*10^5Pa. What is the speed at which the water flows out of the hose at h = 3.0m and h = 2.0m? at what value h does the water stop flowing?


Homework Equations



I'm pretty sure this involves the ideal gas equation of state PV = nrT and maybe the fact that the volume increase or decrease dV with respect to time is equal to the height increase or decrease dh with respect to time...

The Attempt at a Solution



I have tried quite a few things but to be honest I am stumped at how to approach this problem so please help...i strongly appreciate it...

Homework Statement



to find a solution on question 1 is just a ratio and proportion between pressure and height h@3m/p@3m=h@3.5m/P@3.5m, when you get the pressure apply it to the bernoulli's principle or equation then you obtain the velocity because you have a very big tank the initial velocity is zero and your output pressure is zero because it is discharges to the atmosphere "assuming".


2. Homework Equations [/b

this is not an ideal gas because we are talking about water in this problem



The Attempt at a Solution


to obtain the height at when it stop flowing your pressure at that particular height must be atmospheric, apply ratio and poportion approach
 
Last edited:
  • #3
rodeliocueva said:
to obtain the height at when it stop flowing your pressure at that particular height must be atmospheric, apply ratio and poportion approach
,used the same equation you used in the first question
 

FAQ: Question on pressure, volume and rates of change

What is the relationship between pressure and volume?

The relationship between pressure and volume is known as Boyle's Law. It states that at a constant temperature, the pressure and volume of a gas are inversely proportional to each other. This means that as pressure increases, volume decreases and vice versa.

How does pressure affect the rate of change?

Pressure can affect the rate of change in multiple ways. In gases, an increase in pressure typically leads to an increase in the rate of change of volume. This is because higher pressure means more collisions between particles, causing them to move faster and increase in volume. However, in liquids and solids, an increase in pressure can lead to a decrease in the rate of change as it compresses the substance and slows down the movement of particles.

What factors affect pressure?

The factors that affect pressure include the amount of force applied, the area over which the force is applied, and the temperature of the substance. Additionally, the volume and number of particles in a given space can also affect pressure. In liquids and solids, gravity can also play a role in the pressure exerted by the substance.

How is pressure measured?

Pressure is typically measured using a device called a manometer, which consists of a tube filled with a liquid (usually mercury or water) and connected to the substance being measured. The pressure is then determined by the height of the liquid in the tube, as the pressure increases, the height of the liquid also increases.

Can pressure and volume be changed simultaneously?

Yes, pressure and volume can be changed simultaneously. This is known as Charles's Law, which states that at a constant pressure, the volume and temperature of a gas are directly proportional to each other. This means that as the volume increases, the temperature also increases and vice versa.

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