Bernoulli's Equation, Find gauge pressure at 2nd point

In summary, at a certain point in the pipeline, the velocity is 1 m/s and the gauge pressure is 3 x 105 N/m2. At a second point in the line 20 m lower than the first, the liquid in the pipe is water. The velocity of the water at the second point will be double of that at the first point, i.e., 2 m/s. The pressure at the second point is 4.95 x 105 N/m2.
  • #1
Ishraq Begum
13
3

Homework Statement


At a certain point in a pipeline, the velocity is 1 m/s and the gauge pressure is 3 x 105 N/m2. Find the gauge pressure at a second point in the line 20 m lower than the first if the cross-section at the second point is one half that at the first. The liquid in the pipe is water.

Homework Equations


Bernoulli's equation and Equation of continuity.

The Attempt at a Solution


I don't really know where to start
 
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  • #2
Ishraq Begum said:

Homework Statement


At a certain point in a pipeline, the velocity is 1 m/s and the gauge pressure is 3 x 105 N/m2. Find the gauge pressure at a second point in the line 20 m lower than the first if the cross-section at the second point is one half that at the first. The liquid in the pipe is water.

Homework Equations


Bernoulli's equation and Equation of continuity.

The Attempt at a Solution


I don't really know where to start

Try to start writing down the equations with symbols. What will be the velocity of the water at the second point?
 
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  • #3
stockzahn said:
Try to start writing down the equations with symbols. What will be the velocity of the water at the second point?
The velocity of the water at the second point will be double of that at the first point, i.e., 2 m/s
How do you find the gauge pressure??
 
  • #4
Ishraq Begum said:
The velocity of the water at the second point will be double of that at the first point, i.e., 2 m/s
How do you find the gauge pressure??

What does Bernoulli's law state (in case of a water stream without frictional pressure losses)?
 
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  • #5
stockzahn said:
What does Bernoulli's law state (in case of a water stream without frictional pressure losses)?
It states that total energy per unit volume remains constant throughout the flow.
Mathematically,
P + ρgh + 1/2 ρv2 = constant
P = pressure, ρ = density of fluid, h = height of fluid, v = velocity with fluid is flowing
 
  • #6
Ishraq Begum said:
It states that total energy per unit volume remains constant throughout the flow.
Mathematically,
P + ρgh + 1/2 ρv2 = constant
P = pressure, ρ = density of fluid, h = height of fluid, v = velocity with fluid is flowing

Well, that means, that the sum of static, dynamic and hydrostatic pressure at both points are equal. How could you describe this mathematically (e.g. by using subscripts ##_1## and ##_2## for the two different points)?
 
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  • #7
stockzahn said:
Well, that means, that the sum of static, dynamic and hydrostatic pressure at both points are equal. How could you describe this mathematically (e.g. by using subscripts ##_1## and ##_2## for the two different points)?
or P1 + ρgh1 + 1/2 ρv12 = P2 + ρgh2 + 1/2 ρv22

Here, P1 = 3 x 105
ρgh1 = 9.8 x 103 x h
1/2 ρv12 = 1/2 x 13 x 1 = 500
P2 = ? (to be found)
ρgh2 = 9.8 x 103 x (h - 20)
1/2 ρv22 = 2 x 102

⇒ (3x105) + 9.8 x 103 (h - h +20) + (500 - 2 x 103) = P2
⇒ (3 x 105) + (1.96 x 105) + (-1500) = P2
Therefore, P2 = 4.95 x 105 N/m2

That's the answer! Thanks a lot!
 

Related to Bernoulli's Equation, Find gauge pressure at 2nd point

1. What is Bernoulli's Equation and how is it used to find gauge pressure at a second point?

Bernoulli's Equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and height in a fluid flow. It is commonly used to calculate the pressure at a specific point in a flow, known as the gauge pressure, by considering the velocity and height of the fluid at that point.

2. What are the assumptions made in Bernoulli's Equation?

The main assumptions made in Bernoulli's Equation are that the fluid is incompressible, inviscid, and flows along a streamline. This means that the fluid has a constant density, has no internal friction, and follows a smooth and continuous path without crossing or mixing with other fluid particles.

3. Can Bernoulli's Equation be applied to any fluid flow?

No, Bernoulli's Equation is only applicable to steady, inviscid, and incompressible fluid flows. This means that it cannot be used for flows with changing velocity or viscosity, or for compressible fluids like gases.

4. How is gauge pressure different from absolute pressure?

Gauge pressure is the pressure measured relative to atmospheric pressure, while absolute pressure is the total pressure at a point, including the pressure of the atmosphere. Gauge pressure is often used because it is more relevant to practical applications, while absolute pressure is used in theoretical calculations.

5. What are some real-world applications of Bernoulli's Equation?

Bernoulli's Equation has numerous applications in engineering and science, such as in the design of aircraft wings and propellers, the operation of turbines and pumps, and the study of weather patterns and ocean currents. It is also used in medical devices like ventilators and nebulizers, and in everyday phenomena like the flow of water through pipes and the flight of a frisbee.

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