A tube with cross sections at A and B , having areas of 4 mm ^2 and 2 mm ^2 respectively, is kept vertical with B positioned upward. The distance separating A and B is 15 16 cm . Water enters through B at a rate of 1 cm ^3 s ⁻¹ . Determine the speed of the water at A . Note that the speed decreases as the water falls down. Take g = 10 m s ⁻² .

Step-by-step solution

Given that the water falls down and its speed decreases, the water must completely fill the tube. This implies that the flow is steady and the equation of continuity is applicable. According to the equation of continuity, the volume flow rate Q is constant across any cross-section of the tube: Q = A_A v_A = A_B v_B We are given: Volume flow rate, Q = 1 cm ^3 s ⁻¹ Cross-sectional area at A , A_A = 4 mm ^2 = 4 10⁻² cm ^2 Substituting the given values to find the speed of water at A ( v_A ): v_A = Q A_A v_A = 1 4 10⁻²