Question

Water enters through end A with a speed v1 and leaves through end B with a speed v2 of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v1 = v2 for
(a) case I
(b) case II
(c) case III
(d) each case

Answer 1

(d) each case

Explanation:

• As per the equation of continuity, the amount of water that crosses point A over some amount of time is equal to the amount that crosses the point B.  
• Which means, AAV1 =ABV2
• [AA and AB are area at the points of A and B respectively  
• V1 and V2 are velocity of water at the points of A and B respectively]
• So, in the cylindrical tube AB the velocity of water entering into point A and leaving through point B is equal (V1 =V2) as the cross-sectional area at both points are same (AA =AB) for all the three cases.