Water flows through a horizontal tube of variable cross section. The cross-sectional areas at A and B are 4 mm ^2 and 2 mm ^2 respectively. Given that 1 cc of water enters through A per second, compute the speed of the water at B .

Step-by-step solution

According to the equation of continuity, the volume flow rate Q remains constant throughout the tube. Q = A_A v_A = A_B v_B Given, the volume of water entering per second at A is Q = 1 cc/s = 1 cm ^3 /s . The cross-sectional area at B is A_B = 2 mm ^2 = 2 10⁻² cm ^2 . The speed of water at B is v_B . v_B = Q A_B v_B = 1 2 10⁻² cm/s v_B = 100 2 cm/s = 50 cm/s