The viscosity of a fluid is to be measured by an viscometer constructed of two 5 ft long concentric cylinders. the inner diameter of the outer cylinder is 6 in, and the gap between the two cylinders is 0.035 in. the outer cylinder is rotated at 250 rpm, and the torque is measured to be 1.2lbf *ft.
a) determine the viscosity of the fluid.

Explanation:

For this case we need to remember first thet the torque T is defined as:

Where T represent the torque, F the force acting in the inner cylinder and R the radius for the inner cylinder.

For the inner cylinder the force acting can be expressed as:

Where represent the viscosity of the fluid, A the area of the inner cylinder, v represent the tangential velocity and l the thickness of fluid between the two cylinders.

And the tangential velocity for this case can be esxpressed as

The info given is:

from the info given

N= 250 rpm represent the reveolutions per minute

represent the torque given

We can find the surface area for the cylinder with this formula:

And if we replace we got:

Now we can find the tangential velocity like this:

Now we can set up the following equation for the torque:

And we can find the value for the viscosity like this:

And if we replace we got:

answer:

Romans

Explanation:

Hope it helps