Calculating Pressure in a Narrowed Pipe

In summary, the conversation is about using Bernoulli's principle to find the pressure reading in a wide section of a horizontal pipe that narrows smoothly. The equation A_1*F_1=A_2*F_2 is mentioned and the correct equation for this problem is determined to be P1-P2=1/2 (density) (V2^2-V1^2) and A1V1=A2V2. A resource for further understanding of Bernoulli's principle is provided. The correct pressure reading is found to be 5.34 x 10^4.
  • #1
iceman_ch
33
0

Homework Statement



Water flows at through a horizontal pipe that narrows smoothly from 10 cm diameter to 5.0 cm diameter. A pressure gauge in the narrow section reads 50 kPa.

What is the reading of a pressure gauge in the wide section

Homework Equations



A_1*F_1=A_2*F_2

The Attempt at a Solution



I tried to use this equation and it didn't work. I already know the answer is 5.34 x 10^4 but I need to know how to get that answer.
 
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  • #2
Do you know bernoulli's eqn. I think that is what is needed here. Hint: in the narrow section the water must have 4 times the velocity as in the wide section. I'm off for now but maybe others can pick up if you need additional help.
 
  • #3
Let me see if I have the equation correct.

P1-P2=1/2 (density) (V2^2-V1^2)

and

A1V1=A2V2

Is this what you are talking about?
 
  • #4
Yes. Those are correct. You can see the derivation here -

http://en.wikipedia.org/wiki/Bernoulli's_principle
 
  • #5
Thanks for your help this make sense now
 

1. What is pressure in a pipe?

Pressure in a pipe refers to the force exerted by a fluid, such as water or gas, on the walls of the pipe. This pressure is created by the weight of the fluid and is measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (Pa).

2. How is pressure in a pipe calculated?

The pressure in a pipe can be calculated using the equation P = F/A, where P is pressure, F is the force exerted by the fluid, and A is the cross-sectional area of the pipe. This equation assumes that the force is evenly distributed across the entire area of the pipe.

3. What factors affect pressure in a pipe?

The pressure in a pipe is affected by several factors, including the type of fluid flowing through the pipe, the velocity of the fluid, the diameter and length of the pipe, and any obstructions or changes in direction within the pipe.

4. How is pressure in a pipe measured?

Pressure in a pipe can be measured using a pressure gauge, which typically consists of a pressure-sensitive element, such as a diaphragm or spring, and a scale that displays the pressure reading. The gauge is attached to the pipe and measures the force exerted by the fluid on the element.

5. Why is pressure in a pipe important?

Pressure in a pipe is important because it affects the flow of fluids through the pipe. If the pressure is too low, the fluid may not flow at the desired rate, while if the pressure is too high, it can put stress on the pipe and potentially cause damage. Pressure in a pipe is also important in determining the efficiency and performance of various systems, such as plumbing or irrigation systems.

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