Question

Water enters through end A with a speed \[{v_1}\] and leaves through end B with a speed \[{v_2}\] 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\[{v_1} = {v_2}\]for
A. Case I
B. Case II
C. Case III
D. Each case

Answer 1

Hint: Before going to solve this question let us understand what data they have given. They are telling that; the water enters at one end and leaves at other end with a speed \[{v_1}\] and leaves through end B with a speed \[{v_2}\] of a cylindrical tube AB and for that three cases are given. We have \[{v_1} = {v_2}\]. Here, we need to find for which case this equation is applicable.

Complete step by step solution:
In the first case, water enters through end A with a speed \[{v_1}\] and leaves through end B with a speed \[{v_2}\] of a cylindrical tube AB and the water is completely filled and is in a horizontal position. In case II it is vertical with the end A upward and in case III it is vertical with end B upward. We need to find in which case \[{v_1} = {v_2}\].

Here, since the water is incompressible, the volume of water entering end A and leaving through end B per unit time will remain constant in every case and the area of the cross-section of the cylindrical tube will be constant, for each case we get \[{v_1} = {v_2}\].

Hence, option D is the correct answer.

Note: In order to solve this problem it is important to remember the properties of water and how the water behaves in a cylindrical tube AB. And also here the area of cross-section of the cylinder is constant.