General equation of velocity along the pipe

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The discussion focuses on deriving the general expression for fluid velocity in a pipe that expands from a diameter of 0.5m to 1m over a length of 1m. It emphasizes that fluid velocity decreases as pipe diameter increases, suggesting the use of the continuity equation for calculations. Participants are encouraged to verify the dimensional correctness of their equations. There is a request for clarification regarding the visibility of the working diagram associated with the problem. The conversation highlights the importance of clear communication and accurate calculations in fluid dynamics.
foo9008
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Homework Statement


A pipe diameter changes from 0.5m to 1m in a length of 1m in a pipe diffuser . If a discharge Q flows from 0.5m diameter towards 1m diamater , obtain the general expression for velocity at the pipe cross section .

Homework Equations

The Attempt at a Solution


since we know that the velocity of fluid in pipe decreases when the size of pipe increases , So , my working is Velocity at the entrance - (difference in velocity between entrance and exit / area of pipe ) , where the area of pipe has the diameter which increases from the entrance ) , i let is as x in my working . Is my working correct ?
 

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You can simply use equation of continuity.
Check if your equation is dimensionally correct.
 
foo9008 said:

Homework Statement


A pipe diameter changes from 0.5m to 1m in a length of 1m in a pipe diffuser . If a discharge Q flows from 0.5m diameter towards 1m diamater , obtain the general expression for velocity at the pipe cross section .

Homework Equations

The Attempt at a Solution


since we know that the velocity of fluid in pipe decreases when the size of pipe increases , So , my working is Velocity at the entrance - (difference in velocity between entrance and exit / area of pipe ) , where the area of pipe has the diameter which increases from the entrance ) , i let is as x in my working . Is my working correct ?
I just see a diagram. If there is any working associated with it, it is not visible.
 
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SteamKing said:
I just see a diagram. If there is any working associated with it, it is not visible.
sorry , here is it
 

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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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