Question

The pump operates using motor that has a power of 85w if the impeller at b is turning a 150 rev/min determine the maximum shear stress in the 20mm dimeter transmission shaft at a

Answer 1

Answer:

Shear Stress = 3.44 MPa

Step by step explanation:

It is given that:

• Power 'P' = 85 W
• Impeller turns at 150 rev/min
• Diameter = 20 mm

We will use the following formula:

$P=T\omega$

Where P is the power, T is the torque, and ω is the angular velocity.

Therefore,

$T = \frac { P } { \omega } = \frac { 85 } { 150 \frac { r e v } { \min } \left( \frac { 2 \pi r a d } { r e v } \right) \left( \frac { 1 \min } { 60 s } \right) } = 5.411\:Nm$

To calculate the shear stress,

$\tau = \frac { T r } { J }$

Where $\tau$ is the shear stress, T is the torque, r is the distance from center to stressed surface and J is the polar Moment of Inertia.

For a solid shaft, $J = \frac { \pi } { 2 } r ^ { 4 }$

Hence,

$\tau _ { \max } = \frac { T r } { J } = \frac { 5.411 ( 0.01 ) } { \frac { \pi } { 2 } ( 0.01 ) ^ { 4 } } = 3.44\:MPa$