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

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Homework Help Overview

The discussion revolves around a fluid dynamics problem involving water flow in a tapered pipe. Participants are examining how water pressure and velocity change as water moves from a basement to a second floor, considering the effects of elevation and pipe diameter on these parameters.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Bernoulli's equation and the implications of changes in velocity and elevation on pressure. There are attempts to clarify the concept of the constant in Bernoulli's equation and how to calculate pressure at the second floor. Some participants express confusion about their calculations leading to unrealistic pressure values.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and questioning their understanding of the principles involved. Some guidance has been provided regarding the use of Bernoulli's equation and the relationship between flow rate and speed, but no consensus has been reached on the correct pressure value.

Contextual Notes

Participants are working under the assumption that the density of freshwater is 1.0e3 kg/m^3 and are trying to reconcile their results with the known initial pressure of 170 kPa. There is an acknowledgment that pressure cannot be negative, which adds to the complexity of their calculations.

bearhug
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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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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
 
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.
 
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
 

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