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 end B upward. We have v₁ = v₂ for
(a) Case I
(b) Case II
(c) Case III
(d) Each case.

Answer 1

Case I ⇒ Since, the tube is of cylindrical shape, hence, area of cross-section is same. Now, Volume rate of flow is always constant.

Thus, applying equation of continuity,

a₁ × v₁ = a₂ × v₂

v₁ = v₂  [Since, a₁ = a₂].

Case II ⇒ In this case also, Equation of continuity will be valid. Hence, v₁ = v₂. [Whether A is at the top or B, both are having same cross-section, thus it does not make an sense.]

Case III ⇒ In this case also, Equation of continuity will be valid. Hence, v₁ = v₂.

''Hence, Correct answer is option (d). Each case.''

Hope it helps.