Question

A cylindrical tube of a spray pump has a radius r, one end of which has n fine holes each of radius r. If the speed of flow of the liquid in the tube is v, the speed of ejection of the liquid through the hole is?

Answer 1

Area of cross-section of the tube, A = 8 cm2

Speed of water inside the tube, V = 1.25 m/min = 1.25 m/min = 125 cm/min

Diameter of hole, d = 1 mm = 0.1 cm

Area of cross-section of one small hole at the end is, a = πd2/4 = 0.00785 cm2

Let the speed of water through each hole be ‘v’.

So, from equation of continuity, AV = 40(av)

=> v = AV/(40a) = (8)(125)/(40 × 0.00785)

=> v = 3184.7 cm/min

=> v = 31.847 m/min