Question

The cylinder is removed and the original arrangement is restored. A tiny *** of area ( *<<A) is punched on the vertical side of the container at a height h (h < H/2). Determine:

(i) the initial speed of efflux of liquid at the ****.

(ii) the horizontal distance x travelled by the liquid initially.

(iii) the height hm at which the **** should be punched so that the liquid travels the maximum

distance xm initially. Also calculate xm:

(Neglect the air-resistance in these calculations).

Answer 1

(i) Let vA and vB be velocity of fluids at points A and B.

(ii) Time t taken by liquid to fall through height h under g with zero initial velocity,

t =√2h/g

Horizontal distance x = vBt

(iii) To find height h at which x is max, dh/dx = 0