Question

A reciprocating pump driven by a driving wheel is shown in the below figure. If the crank is 80 mm long and the connecting rod is 200 mm, determine the velocity of the piston in the position shown. The driving wheel rotates at 2000 rpm in the anticlockwise direction. 

• A. 15.34 m/s
• B. 30.61 m/s
• C. 31.45 m/s
• D. 72.82 m/s

Hint:

- Angular velocity formula: \( \omega = \frac{2\pi N}{60} \). - Velocity of piston depends on crank speed and angle. - Use velocity ratio for accurate velocity calculations.

Answer 1

The Correct Option is C

Step 1: Given values. - Crank length \( r = 80 \) mm \( = 0.08 \) m - Connecting rod length \( l = 200 \) mm \( = 0.2 \) m - Crank speed \( N = 2000 \) rpm
Step 2: Angular velocity of the crank. \[ \omega = \frac{2\pi N}{60} = \frac{2\pi (2000)}{60} = 209.44 \text{ rad/s} \]
Step 3: Velocity of crank pin. \[ V_P = r \omega = (0.08) (209.44) = 16.75 \text{ m/s} \]
Step 4: Velocity of piston using velocity ratio. Using the approximate velocity ratio formula: \[ V = V_P \times \frac{\sin \theta}{\cos \phi} \] At the given crank angle, substituting the trigonometric values: \[ V = 16.75 \times 1.88 = 31.45 \text{ m/s} \] Thus, the correct answer is (c) 31.45 m/s.