Pressure in a pipe of varying size

In summary, the picture serves as a guide for understanding the relationship between pressure (P) and speed (vi) of a non-viscous incompressible fluid at five locations. The options for each statement are greater than, less than, or equal to. Using Bernoulli's equation, it can be determined that v1 is equal to 2v3, P1 is greater than P2, P1 is greater than P4, P3 is less than P4, v4 is greater than v5, v1 is greater than v2, and P4 is greater than P5. The question requires selecting the correct options for each statement.
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Homework Statement



Use the picture as a guide. P is the pressure in the pipe, and vi is the speed of a non-viscous incompressible fluid at locations i = 1,2,3,4,5.(For each statement select correctly)

http://lon-capa.phy.cmich.edu/res/msu/physicslib/msuphysicslib/33_Fluids2_Bernoulli/graphics/prob07_Bernoulli.gif

Options are: Greater than, less than and Equal to
v1 is ... 2v3.
P1 is ... P2.
P1 is ... P4.
P3 is ... P4.
v4 is ... v5.
v1 is ... v2.
P4 is ... P5.

Homework Equations



Bernoulli's: P+1/2pv^2+pgh=Constant

The Attempt at a Solution



-Equal to
-Greater than
-Greater than
-Less than
-Greater than
-Greater than
-Greater than

This is my most recent attempt. I have 20 attempts and have used 5, but I still don't see where I am going wrong here. The assignment is due at midnight and this is my last question (current time is 10:15PM), so this is my last option.
 
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1. What causes pressure in a pipe of varying size?

The pressure in a pipe of varying size is caused by the force exerted by the fluid inside the pipe on the walls of the pipe. This force is a result of the fluid's weight and velocity.

2. How does the size of the pipe affect the pressure inside?

The size of the pipe directly affects the pressure inside. As the pipe size increases, the pressure decreases and vice versa. This is because a larger pipe has more surface area, causing the force to spread out and decrease the pressure.

3. What is the relationship between pressure and velocity in a pipe of varying size?

According to Bernoulli's principle, as the velocity of a fluid increases, the pressure decreases. In a pipe of varying size, as the velocity of the fluid changes due to changes in pipe size, the pressure also changes accordingly.

4. How does the shape of the pipe affect the pressure inside?

The shape of the pipe does not have a direct effect on the pressure inside. However, different shapes may cause changes in the velocity of the fluid, which can then affect the pressure according to Bernoulli's principle.

5. Can the pressure in a pipe of varying size be controlled?

Yes, the pressure in a pipe of varying size can be controlled by adjusting the velocity of the fluid or by using valves and regulators to regulate the flow of the fluid. The size and shape of the pipe can also be altered to control the pressure.

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