Is My Flow Rate Calculation Correct?

[Ross891]

Help with flow rates... part 2

Homework Statement

A convergent divergent nozzle has an initial diameter of 1m this then reduces in size to 0.5 and finally expands to 2m the initial flow rate 22 m^3/s and the relative density of the fluid is 0.45

Homework Equations

The Attempt at a Solution

I worked out the areas of the first two diameters

∏X1^2/4 = 0.785

∏X0.5^2/4=0.196


Next I'd divide the small answer into the large one.

0.785/0.196=4.005

Then I multiplied this answer by the previous flow,rate

4.005x22=88m^3/s

Now the flow rate through the 0.5 diameter is 88m^3/s

To work out the velocity of flow rearrange the equation of flow rate flow rate/surface area

88/0.196=448.97

And I worked out the velocity of diameter a too.

22/0.785=28.02

Next I worked out the surface area of the 2m diameter

∏X2^2/4=3.141

Next I divided the surface area of the 0.5m diameter Into the 2m diameters surface area.

3.141/0.196=16.02

Now use the rearranged flowrate equation that I used earlier to get the velocity of flow.

16.02/3.141=5.1

Velocity for diameters:

1m=28.02m/s
0.5m=91.66m/s
2m=5.1m/s



For part b it is relatively easy

Surface area x relative density x velocity

For dia 1m 0.785x0.45x28.02= 9.891 kg/s
For dia 0.5m 0.196x0.45x91.66= 8.08 kg/s
For dia 2m 3.141x0.45x5.1=7.2063


I'm a little rusty to say the least on flowrates and I would appreciate comments on weather This is right?

 

[haruspex]

Then I multiplied this answer by the previous flow,rate
4.005x22=88m^3/s
Now the flow rate through the 0.5 diameter is 88m^3/s

If 22 m³/s of water is entering the pipe, but 88m³/s is flowing past some point along the path, 66m³/s is magically appearing out of nowhere.
As the pipe changes width, the linear flow rate changes, but the mass flow rate cannot, so (unless it's compressible) neither can the volumetric flow rate.

 

[Ross891]

If 22 m³/s of water is entering the pipe, but 88m³/s is flowing past some point along the path, 66m³/s is magically appearing out of nowhere.
As the pipe changes width, the linear flow rate changes, but the mass flow rate cannot, so (unless it's compressible) neither can the volumetric flow rate.

That's interesting and It makes sense.

It could well be that the flow rate has once again been mixed up with velocity of flow. Ill check with my tutor.

 

[haruspex]

It could well be that the flow rate has once again been mixed up with velocity of flow. Ill check with my tutor.

There was nothing obviously wrong with the problem as stated, but you left out what the questions were. If it asked for the velocity at various points then it would be fine.

 

[Ross891]

There was nothing obviously wrong with the problem as stated, but you left out what the questions were. If it asked for the velocity at various points then it would be fine.

I does ask for the velocities I forgot to post that part thanks a lot!