How Does Water Pressure Change with Velocity and Elevation in a Tapered Pipe?

[bearhug]

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.

 

[Andrew Mason]

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

 

[bearhug]

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.

 

[Andrew Mason]

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