Change in Pressure in a Pipe

In summary, the pressure in the pipe when it reaches the desalination plant at a height of 5.00 m above the ocean surface is 19400 Pa, calculated using the formula P2 = P1 + p*g*(y1-y2). The pipe has a width of 2.00 m and is used to transport salt water from the ocean into the plant, with a pump pushing the water in at a depth of 1.00 m below the surface with a pressure of 80 kPa. The density of salt water is 1030 kg/m^3.
  • #1
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Homework Statement


A pipe has a square cross section and a width of 2.00 m and is used to transport salt water from the ocean into a desalination plant. If a pump pushing the water into the pipe at a depth of 1.00 m below the surface of the ocean does so with a pressure of 80 kP a, and the dimensions of the pipe doesn’t change, what is the pressure in the pipe when it gets into the plant at a height of 5.00 m above the surface of the ocean?

Homework Equations


A*v=A*v
P1+1/2p*v^2 + pgy = P2 + 1/2p*v^2 + pgy
P_2 = P_1 + p*g*(y_1 - y_2)[/B]
p_saltwater = 1030 kg/m^3

The Attempt at a Solution


P_2 = P_1 - p*g*(4)
= 80000 + (1030)(9.81)(4) = 39582.8 [/B]
 
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  • #2
mailmas said:
P_2 = P_1 - p*g*(4)
4? Read the question more carefully.
 
  • #3
haruspex said:
4? Read the question more carefully.
80000 - (1030)(9.81)(6) = 80000 - 60625.8 = 19374.2
 
  • #4
mailmas said:
80000 - (1030)(9.81)(6) = 80000 - 60625.8 = 19374.2
Looks better, but you quote too many significant figures.
 
  • #5
haruspex said:
Looks better, but you quote too many significant figures.
19400 Pa
 
  • #6
mailmas said:
19400 Pa
Looks fine.
 
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Likes mailmas

What is meant by "change in pressure" in a pipe?

The change in pressure in a pipe refers to the difference in pressure between two points within the pipe. This change can be caused by various factors such as flow rate, pipe size, and obstructions in the pipe.

How does the change in pressure affect the flow of fluid in a pipe?

The change in pressure directly affects the flow of fluid in a pipe. An increase in pressure will result in a higher flow rate, while a decrease in pressure will result in a lower flow rate. This is known as Bernoulli's principle.

What factors can cause a change in pressure in a pipe?

There are several factors that can cause a change in pressure in a pipe, including changes in elevation, changes in pipe diameter, and the presence of obstacles or blockages in the pipe.

How is the change in pressure measured in a pipe?

The change in pressure in a pipe is typically measured using a pressure gauge, which displays the pressure in units of force per unit area (such as psi or kPa). This gauge can be placed at different points along the pipe to measure the change in pressure.

What are some practical applications of understanding the change in pressure in a pipe?

Understanding the change in pressure in a pipe is crucial for many industries, such as plumbing, HVAC, and oil and gas. It allows for proper design and maintenance of piping systems, and can also help in detecting and resolving any issues that may arise, such as leaks or blockages.

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