259 a concentric cylinder viscometer may be formed by...

2.59 A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitting cylin- ders. For small clearances, a linear velocity profile may be assumed in the liquid filling the annular clearance gap. A viscometer has an inner cylinder of 75 mm diameter and 150 mm height, with a clearance gap width of 0.02 mm. A torque of 0.021 N·m is required to turn the inner cylinder at 100 rpm. Determine the viscosity of the liquid in the clearance gap of the viscometer. H a r Cord Pulley. R M V m

Transcript

00:01 Hello, in this question we are given that a concentric cylinder viscometer may be found by rotating the inner member of the pair closely fitting cylinders.

00:11 The situation is something like this.

00:13 This is the exterior cylinder.

00:21 There is one more cylinder fitted inside it and now the inner cylinder is rotated while filling the fluid in between these two.

00:40 Here fluid is filled.

00:43 Let me change color over here.

00:46 Here the fluid is filled.

00:51 As we know the sear stress is mu dv over d y and force could be written as area into the sear stress and torque could be written as force into distance that is the perpendicular distance as we know.

01:18 Okay so over here we'll also t if this external point is stationary and the inner one is moving.

01:28 So dv for this particular distance if this is the distance t thickness, okay.

01:34 So dy here would be t and dv here would be what the speed of the inner because here speed is zero and here speed is omega into r.

01:43 Okay so dv would be omega into r.

01:47 So now we will put our values over here as we are given everything in this question.

01:53 So the torque over here is 0 .021 newton that must be equal to distance distance is what the radius okay so the radius is 75 by 2 75 by 2 into 10 to the power minus 3 because we will write everything in the standard units okay we will convert millimeters to meter now the force would be tau into area.

02:30 So let me first write the area.

02:32 Area would be 2 pi r or we can say pi into d into l...

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