How to calculate flow rate from a parabolic velocity profile

[sehrish shakir]

hello!
i was provided by the radii from 0 to 5 cm and a parabolic profile is also given .. in numeric form i was asked to calculate the flow rate how to understand it to solve further kindly help
...

 

[Chestermiller]

hello!
i was provided by the radii from 0 to 5 cm and a parabolic profile is also given .. in numeric form i was asked to calculate the flow rate how to understand it to solve further kindly help
...

Please provide more detail about the locations where the velocity is provided, and the velocity values.

 

[sehrish shakir]

Thank you for kind response sir ,
it was a question in exam ... like
r=0,1,2,3,4,5
v=2,1.92,1.68,1.28,0.72,0
numerical values may be some digits different but i need to understand a problem .
now if diameter is 10cm then calculate the flow rate ?

 

[Chestermiller]

You said that the profile is parabolic. Do you know how to determine the equation for the parabola that satisfies this data? If you knew the equation for the parabola of v vs r, would you know how to determine the volumertic flow rate?

 

[sehrish shakir]

Vz\Vm=2(1-r^2/R^2)
this is the relation
Q=A*v
but how to initiate ?
should i specified the boundary condition then integerate or can do some numerical analysis to evaluate integeral or find out the mean value of velocity then proceed ...

 

[sehrish shakir]

i assumed it is parabolic as laminar has parabolic profile ..flow was laminar

 

[Chestermiller]

Vz\Vm=2(1-r^2/R^2)
this is the relation
Q=A*v
but how to initiate ?

No.
$$Q=\int_0^R{v_z(2\pi r)dr}$$
Does this make sense?

 

[sehrish shakir]

No.
$$Q=\int_0^R{v_z(2\pi r)dr}$$
Does this make sense?

thank you for reply sir,
yes i got it, it is the total flow rate through duct .