Question

A shaft 70 mm in diameter is being pushed at a speed of 400 mm/s through a bearing sleeve 70.2 mm in diameter and 250 mm long. The clearance, assumed uniform, is filled with oil with kinematic viscosity v = 0.005 m²/s and density p= 900 kg/m². Find the force exerted by the oil on the shaft.

Answer 1

F=989.6 N

Step-by-step explanation:

Given that

Diameter of shaft = 70 mm

Diameter of bearing sleeve =70.2 mm

So clearance h=0.1 mm

Speed V= 400 mm/s

Length of shaft = 250 mm

`\\u =0.005\ (m^2)/(s)\ , \rho=900\ (kg)/(m^3)`

We know that

`\mu =\rho*\\u`

μ= 900 x 0.005 Pa-s

μ= 4.5 Pa-s

As we know that

From Newton's law of viscosity ,the shear stress given as follows

`\tau =\mu (dU)/(dy)`

We also know that

Force = shear stress x area

Now by putting the values

`\tau =4.5* (400)/(0.1)`

`\tau=18,000 Pa`

So force

F= 18,000 x π x 0.07 x 0.25

F=988.6 N