Question

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm². The area of cross section at the oulet is 10 mm². If the piston is pushed at a speed of 4 cm s^-1, the speed of outgoing fluid is ______ cm s^-1.

Answer 1

Correct Answer: 80

By the equation of continuity: \[ A_1 V_1 = A_2 V_2 \] Where \( A_1 \) and \( A_2 \) are the areas of cross-section at the piston and the outlet, and \( V_1 \) and \( V_2 \) are the velocities at the piston and the outlet respectively. Given: \[ A_1 = 2 \, \text{cm}^2, \quad V_1 = 4 \, \text{cm/s}^{-1}, \quad A_2 = 10 \, \text{mm}^2 = 10 \times 10^{-2} \, \text{cm}^2 \] Substituting in the continuity equation: \[ 2 \times 4 = (10 \times 10^{-2}) \times V_2 \] Solving for \( V_2 \): \[ V_2 = \frac{2 \times 4}{10 \times 10^{-2}} = 80 \, \text{cm/s}^{-1} \] Thus, the speed of the outgoing fluid is 80 cm/s\(^-1\).