Question

Consider water falling from a faucet. At the faucet opening, water flows with a velocity of 0.75 m/s and a diameter of 4 cm. What is the diameter of the water flow after the water has fallen 53 cm. Assume the water is incompressible.

a. 2.36 cm

b. 6 cm

c. 1.9 cm

d. 2.99 cm

e. 1.61 cm

Correct answer is C.

Answer 1

Here ,

initial speed of flow , v1= 0.75 m/s

height , h = 53 cm = 0.53 m

initial diameter , d1 = 4 cm

radius , r1 = 2 cm = 0.02 m

let the final speed is v2

Using third equation of motion

v2^2 - v1^2 = 2 * a * h

v2^2 - 0.75^2 = 2 * 0.53 * 9.8

v2 = 3.31 m/s

NOw , for the final diameter d2

Using equation of continuity

v1 * A1 = v2 * A2

A is the area of cross section

0.75 * pi *(4/2)^2 = 3.31 *pi *(d2/2)^2

d2 = 1.904 cm

the diameter after falling 53 cm is c) 1.9 cm