need help with a Fluids Engineering problem
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Postmaster
Joined: Mar 2003
Posts: 4,513
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From: La Tech University, La
need help with a Fluids Engineering problem
I need to derive the formula for a rotating cylinder viscometer neglecting end effects.
I know the formula:
T=torque
w=rotational velocity in rads
L=depth of fluid
u=viscocity
R1=radius of rotating cylinder
R2=radius of fixed outer cylinder
Formula:
T=4*(pi)*w*L*u*[(R1^2*R2^2)/(R2^2-R1^2)]
I just cannot figure out how to derive the dang thing.
I know the formula:
T=torque
w=rotational velocity in rads
L=depth of fluid
u=viscocity
R1=radius of rotating cylinder
R2=radius of fixed outer cylinder
Formula:
T=4*(pi)*w*L*u*[(R1^2*R2^2)/(R2^2-R1^2)]
I just cannot figure out how to derive the dang thing.
Postmaster
Joined: Aug 2004
Posts: 4,004
Likes: 1
From: North of Boston MA
The formula looks a little strange since it is solving for Torque. Wouldn't viscosity be your only unknown?
The hard part will be getting all your units in order and cancelling out those you don't need. It looks like all the formula involves is a difference in surface area between the cylinders, a difference in volumes (L is a common factor in these, as is pi), the rotational speed (radians per second) and the torque (newton-meters?). It doesn't look to be that bad.
Slow day at work today, let me see if I can make this work....
The hard part will be getting all your units in order and cancelling out those you don't need. It looks like all the formula involves is a difference in surface area between the cylinders, a difference in volumes (L is a common factor in these, as is pi), the rotational speed (radians per second) and the torque (newton-meters?). It doesn't look to be that bad.
Slow day at work today, let me see if I can make this work....
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