Water pressure and speed

In summary: I already have the speed. 3.9m/s and I'm using the density of freshwater being 1.0e3 kg/m^3. I know I'm calculating something wrong I keep coming up with a huge number or a negative number for pressure which, can't be negative right? and needs to be less than 170 kPa.The pressure in SI units is 170000 N/m^2 or Pa.
  • #1
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A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what is the (a) speed, and (b) water pressure, at the second floor?

the speed I got to be 3.9m/s now I'm having a hard time finding pressure.
I know that pressure decreases as velocity increased and as altitude increases, both of which are happening here. So I know that the pressure on the second floor is less than 170kPa. I'm trying to use Bernoulli's equation P + 1/2pv^2 + pgy=constant. First of all, what is the constant. My book doesn't explain this at all just has it appear in this equation. One way I approached the problem is by using the equation P1 - P2 = pgh and solving for P2 but I'm not sure if this is anywhere close to right. Any help is appreciated.
 
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  • #2
bearhug said:
A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what is the (a) speed, and (b) water pressure, at the second floor?

the speed I got to be 3.9m/s now I'm having a hard time finding pressure.
I know that pressure decreases as velocity increased and as altitude increases, both of which are happening here. So I know that the pressure on the second floor is less than 170kPa. I'm trying to use Bernoulli's equation P + 1/2pv^2 + pgy=constant. First of all, what is the constant. My book doesn't explain this at all just has it appear in this equation. One way I approached the problem is by using the equation P1 - P2 = pgh and solving for P2 but I'm not sure if this is anywhere close to right. Any help is appreciated.

The constant is the value of the Bernoulli equation in the basement where h = 0.

But that does not give you the speed. The speed is determined by the rate of flow. Work out the speed on the second floor from the rate of flow. Then put that speed in the Bernoulli equation along with the height to determine the pressure on the second floor.

AM
 
  • #3
I already have the speed. 3.9m/s and I'm using the density of freshwater being 1.0e3 kg/m^3. I know I'm calculating something wrong I keep coming up with a huge number or a negative number for pressure which, can't be negative right? and needs to be less than 170 kPa.
 
  • #4
bearhug said:
I already have the speed. 3.9m/s and I'm using the density of freshwater being 1.0e3 kg/m^3. I know I'm calculating something wrong I keep coming up with a huge number or a negative number for pressure which, can't be negative right? and needs to be less than 170 kPa.

I get about 88 kPa for the pressure. The pressure in SI units is 170000 N/m^2 or Pa.

AM
 

1. What is water pressure?

Water pressure is the force exerted by a body of water on its surroundings, typically measured in pounds per square inch (psi). It is caused by the weight of the water above a given point and is dependent on the depth and density of the water.

2. How does water pressure affect the speed of water?

Water pressure plays a significant role in determining the speed of water. The higher the water pressure, the faster the water will flow. This is because the force of the water pushing against its surroundings creates a driving force that propels it forward.

3. What factors affect water pressure?

Several factors can affect water pressure, including the depth of the water, the density of the water, and the force of gravity. Other factors such as temperature and salinity can also play a role in water pressure.

4. How is water pressure measured?

Water pressure is typically measured using a pressure gauge, which is a device that measures the force applied by the water on a specific area. It is usually expressed in pounds per square inch (psi) or kilopascals (kPa).

5. How does water speed vary with depth?

The speed of water typically increases with depth as the water pressure increases. This is because the weight of the water above a certain depth increases, resulting in a higher pressure and faster flow. However, other factors such as the shape of the body of water and any obstacles in its path can also affect water speed at different depths.

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