A slipper (slider) and plate (guide), both 0.5 m wide, constitutes a bearing as shown in Fig. 8.20. Density of the fluid, $\rho=9.00 \mathrm{~kg} / \mathrm{m}^{3}$ and viscosity, $\mu=0.1 \mathrm{Ns} / \mathrm{m}^{2}$ .

Find out the (i) load carrying capacity of the bearing, (ii) drag, and (iii) power lost in the bearing.

Question

A slipper (slider) and plate (guide), both 0.5 m wide, constitutes a bearing as shown in Fig. 8.20. Density of the fluid, $\rho=9.00 \mathrm{~kg} / \mathrm{m}^{3}$ and viscosity, $\mu=0.1 \mathrm{Ns} / \mathrm{m}^{2}$ .

Find out the (i) load carrying capacity of the bearing, (ii) drag, and (iii) power lost in the bearing.

Accepted Answer

(i) Considering the width as b and using Eq. (8.82) for the load carrying capacity,

[latex] P=\frac{6 \pi U l^{2} b}{\left(h_{1}-h_{2} ight)^{2}}\left[\ln \frac{h_{1}}{h_{2}}-2 \frac{h_{1}-h_{2}}{h_{1}+h_{2}} ight] [/latex]

[latex] =\left[\frac{6 imes 0.1 imes 1 imes 0.2 imes 0.2 imes 0.5}{(0.005-0.002)^{2}} ight] imes\left[\ln \frac{0.005}{0.002}-2 \frac{0.005-0.002}{0.005+0.002} ight] [/latex]

[latex] =\frac{0.012}{9.0 imes 10^{-6}}(0.9163-0.8571)=78.93 \mathrm{~N} [/latex]

(ii) Making use of Eq. (8.84) for width b, the drag force may be written as

[latex] D=\frac{\mu U l b}{h_{1}-h_{2}}\left[4 \ln \frac{h_{1}}{h_{2}}-6 \frac{h_{1}-h_{2}}{h_{1}+h_{2}} ight] [/latex]

[latex] =\frac{0.1 imes 1 imes 0.2 imes 0.5}{(0.005-0.002)}\left[4 \ln \frac{0.005}{0.002}-6 \frac{0.005-0.002}{0.005+0.002} ight] [/latex]

[latex] =\frac{0.01}{0.003}(3.6651-2.5714)=3.645 \mathrm{~N} [/latex]

(iii) Power lost = Drag × Velocity

[latex] =3.645 imes 1=3.645 \mathrm{~W} [/latex]

Question 8.10: A slipper (slider) and plate (guide), both 0.5 m wide, const...

Related Answered Questions

Verified Answer:

For the following thrust bearing (Fig. 8.22), show that the force on the straight slider in the x direction is the same as that on the guide. ...

Verified Answer:

A cylindrical journal bearing supports a load directed vertically upwards, with the shaft rotating clockwise. Sketch the position of the shaft centre with respect to that of the bearing (hole), if no cavitation is present. Give explanation. No equations are required. ...

Verified Answer:

Consider steady flow of an incompressible Newtonian fluid (density = ρ, viscosity = μ) between two infinitely long concentric circular cylinders of inner radius a and outer radius b (Fig. 8.17). Both the cylinders rotate with the same angular velocity w. In addition, the inner cylinder moves ...

Verified Answer:

The velocity distribution for a fully developed laminar flow in a pipe is given by vz = – R^2 / 4 μ . ∂p / ∂z [ 1 – ( r / R )^2 ] Determine the radial distance from the pipe axis at which the velocity equals the average velocity ...

Verified Answer:

In the laminar flow of a fluid in a circular pipe, the velocity profile is exactly a parabola. The rate of discharge is then represented by volume of a paraboloid. Prove that for this case the ratio of the maximum velocity to mean velocity is 2. ...

Verified Answer:

The analysis of a fully developed laminar flow through a pipe can alternatively be derived from control volume approach. Derive the expression vz = R^2 / 4 μ ( – dp / dz ) ( 1 – r^2 / R^2 ) accordingly. Fig. 8.15 Fully developed laminar flow through a pipe ...

Verified Answer:

A continuous belt (Fig. 8.13) passing upward through a chemical bath at velocity U0, picks up a liquid film of thickness h, density ρ, and viscosity μ. Gravity tends to make the liquid drain down, but the movement of the belt keep the fluid from running off completely. Assume that the flow is ...

Verified Answer:

Water at 60°C flows between two large flat plates. The lower plate moves to the left at a speed of 0.3 m/s. The plate spacing is 3 mm and the flow is laminar. Determine the pressure gradient required to produce zero net flow at a cross section. (μ = 4.7 × 10^–4 Ns/ m^2 at 60 °C) ...

Verified Answer:

Verified Answer: