Why Doesn't the Flow Rate Change When a Vane is Moving in a Pipe?

[foo9008]

Homework Statement

for part c , why when the vane is moving , the flow rate doesn't change ? ?

Homework Equations

The Attempt at a Solution

The flow rate is given by the formula Q=Av , where A = area , v = velocity . IMO , when the velocity of vane change , the flow rate is no longer 0.687kg/s , it should be 0.68kg/s = (10^3)(A)(24) , A= 2.83x10^-5 (m^2) , so the new Q should be pa(v-u) = (10^3)(2.83x10^-5)(24-8) = 0.453kg/s , am i right

 

[Simon Bridge]

for part c , why when the vane is moving , the flow rate doesn't change ? ?

Because it says so in the problem statement.
Why would you expect it to be different?

If you are in a river or out of a river, is the flow rate of the river affected?

 

[foo9008]

Because it says so in the problem statement.
Why would you expect it to be different?

If you are in a river or out of a river, is the flow rate of the river affected?

in part b , the author changed the flow rate because of the vane is moving at 8m/s , why wouldn't the flow rate in part c also change ?

 

[Simon Bridge]

Excuse me, I misread: in part (b) the flow rate is unchanged - the water still leaves the pipe at the same mass rate.
However, the rate that the water hits the single vane is lower because the relative velocity is lower because the vane is moving away.

In part (c) the single vane is replaced by "the set of vanes". What is special about the set of vanes?
Please stop posting pictures of working, hardly anyone will read it unless you type it out.

Why not work through the problem yourself and show your reasoning instead of trying to decipher what the author was trying to do?

 

[foo9008]

Excuse me, I misread: in part (b) the flow rate is unchanged - the water still leaves the pipe at the same mass rate.
However, the rate that the water hits the single vane is lower because the relative velocity is lower because the vane is moving away.

In part (c) the single vane is replaced by "the set of vanes". What is special about the set of vanes?
Please stop posting pictures of working, hardly anyone will read it unless you type it out.

Why not work through the problem yourself and show your reasoning instead of trying to decipher what the author was trying to do?

why not the situation in b same as the situation in c ? in situation c , the author means replacing the vane with the new vane moving with 8ms^-1 . ( the original moving vane is not moving , correct me if i am wrong)

 

[Simon Bridge]

why not the situation in b same as the situation in c ? in situation c , the author means replacing the vane with the new vane moving with 8ms^-1 . ( the original moving vane is not moving , correct me if i am wrong)

That is not how I am reading the question... I'll just make sure we are both looking at the same thing:
It says:
A water jet strikes on a vane at 150$^\circ$. If water flows and velocity are 0.68kg/s and 24m/s respectively, calculate:
(a) resultant force at a stationary vane
(b) resultant force at a vane moving at 8m/s in the jet direction
(c) power output if (b) is replaced by the set of vanes

So, initially the vane is not moving - that is part (a). That vane is replaced by one that is moving - that is part (b). In part (c) the single moving vane is replaced by "the set of vanes", and changes the calculation required from force to power ... so what is special about the set of vanes that it will produce a power output?
Do you have a picture of the set of vanes in question?

I had a bit of trouble following the working in the answers provided though.

 

[haruspex]

IMO , when the velocity of vane change , the flow rate is no longer 0.687kg/s

I agree, and if I'm reading post #4 correctly, so does Simon.
I cannot make sense of the question in part c. The reference to 'the' set of vanes implies there is further information that you have not quoted, probably the number of vanes. However, the calculation of power you posted still only considers one vane, and appears to be appropriate for the circumstances in b, no replacement necessary (except, as noted, the answer should be 2/3 that given).

 

[foo9008]

I agree, and if I'm reading post #4 correctly, so does Simon.
I cannot make sense of the question in part c. The reference to 'the' set of vanes implies there is further information that you have not quoted, probably the number of vanes. However, the calculation of power you posted still only considers one vane, and appears to be appropriate for the circumstances in b, no replacement necessary (except, as noted, the answer should be 2/3 that given).

do u agree that the flow rate should be 0.453kg/s as in b ? sorry , that's all the info i have . The author only gave that ,

 

[haruspex]

do u agree that the flow rate should be 0.453kg/s as in b ? sorry , that's all the info i have . The author only gave that ,

Yes, 0.68 x 2/3 = 0.453...

 

[Simon Bridge]

... it's the suggestion that there is extra information that is not given that is the problem.
By the calculation - there is no replacement needed, so why say there was a replacement?
Why mention "the" vanes anyway?

I was thinking that maybe the assembly of vanes was like a turbine or a water-wheel, so it will remain in place and turn instead of moving away.

 

[haruspex]

I was thinking that maybe the assembly of vanes was like a turbine or a water-wheel, so it will remain in place and turn instead of moving away.

That doesn't get it back to the conditions of a).
Given the part b), my guess would be that the wheel turns in the plane of the jet, so when working it does move away from it.
Even if you take the plane of the wheel as orthogonal to the jet, the strike angle means that the wheel's rotation has an effective component of motion in the direction of the jet, so it still moves away, if rather obliquely.

 

[Simon Bridge]

... and it changes a lot of things. Still - I think I've seen a windmill type arrangement done in approximation like that.
We are basically trying to second guess what the person setting the question was thinking about when they wrote the question, without any further information.
Seems likely, from the later discussion, that the problem setter has made some sort of mistake ... I'm just not confident enough that I have enough information to decide which mistake, if any, was made.

I would have liked to see foo9008 describe the approach to the problem.