General equation of velocity along the pipe

In summary, the problem involves a pipe diffuser with a change in diameter from 0.5m to 1m over a length of 1m. The goal is to find the general expression for velocity at the pipe cross section, with a discharge Q flowing from the smaller diameter towards the larger diameter. The suggested approach is to use the equation of continuity and check the dimensional correctness of the working.
  • #1
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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  • #2
You can simply use equation of continuity.
Check if your equation is dimensionally correct.
 
  • #3
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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  • #4
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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1. What is the general equation of velocity along the pipe?

The general equation of velocity along the pipe is given by the formula v = Q/A, where v is the velocity of the fluid, Q is the volume flow rate, and A is the cross-sectional area of the pipe.

2. How is the general equation of velocity along the pipe derived?

The equation is derived from the continuity equation, which states that the volume flow rate of a fluid is constant at any point in a closed system. By rearranging the equation and substituting for the cross-sectional area of a pipe, we can arrive at the general equation of velocity along the pipe.

3. What are the units of the variables in the general equation of velocity along the pipe?

The velocity v is typically expressed in meters per second (m/s), the volume flow rate Q is measured in cubic meters per second (m^3/s), and the cross-sectional area A is given in square meters (m^2).

4. Can the general equation of velocity along the pipe be applied to any type of fluid?

Yes, the general equation can be applied to any type of fluid, whether it is a liquid or a gas. However, it is important to note that the equation assumes the fluid is incompressible and the flow is steady.

5. How does the general equation of velocity along the pipe change with changes in flow rate or pipe diameter?

If the flow rate increases, the velocity and cross-sectional area will also increase, resulting in a constant ratio and no change in the velocity. However, if the pipe diameter is reduced, the velocity will increase due to a decrease in cross-sectional area, and vice versa.

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