Calculation of Power Lost in the Bearing

Given data:
- Viscosity of the oil film (μ) = 6 poise
- Diameter of the shaft (D) = 0.4 m
- Rotational speed of the shaft (N) = 190 r.p.m
- Length of the sleeve (L) = 90 mm
- Thickness of the oil film (h) = 1.5 mm

Conversion of Units:
To perform the calculations, it is necessary to convert the given units to a consistent system. Since the viscosity is given in poise, it needs to be converted to Pascal-seconds (Pa.s) using the conversion factor 1 poise = 0.1 Pa.s. Similarly, the length of the sleeve and the thickness of the oil film need to be converted to meters.

1 poise = 0.1 Pa.s
90 mm = 0.09 m
1.5 mm = 0.0015 m

Calculation of Oil Film Velocity:
The oil film velocity (V) can be calculated using the formula:

V = π * D * N / 60

Where:
π = 3.14 (approximation of the mathematical constant π)
D = Diameter of the shaft
N = Rotational speed of the shaft in revolutions per minute (r.p.m)

Substituting the given values:
V = 3.14 * 0.4 * 190 / 60

Calculation of Shear Stress:
The shear stress (τ) in the oil film can be calculated using the formula:

τ = μ * V / h

Where:
μ = Viscosity of the oil film
V = Oil film velocity
h = Thickness of the oil film

Substituting the given values:
τ = 6 * (3.14 * 0.4 * 190 / 60) / 0.0015

Calculation of Power Lost:
The power lost in the bearing (P) can be calculated using the formula:

P = τ * A * L

Where:
P = Power lost in the bearing
τ = Shear stress in the oil film
A = Cross-sectional area of the oil film
L = Length of the sleeve

The cross-sectional area of the oil film (A) can be calculated using the formula:

A = π * D * h

Substituting the given values:
A = 3.14 * 0.4 * 0.0015

Finally, substituting the values of τ, A, and L into the power lost formula, we can calculate the power lost in the bearing (P).

P=716w