Question

If you turn on a water faucet so that the water flows smoothly, you should observe that the cross-sectional area of the water stream decreases as the stream drops. At a particular point, the flow speed is 40.0 cm/s and the stream has a cross-sectional area of 2.00 cm². Use g = 9.80 m/s². At a point 7.00 cm below the first point, determine the following.

(a) the flow speed
cm/s

(b) the cross-sectional area of the stream
cm²

Answer 1

The water stream is composed of water molecules moving together. As compared to motion of a solid object like a ball or stone, there are large number of connected molecules getting accelerated due to gravity. Hence the motion of the whole stream is defined by the same kinematic equations (equations of motion) as the ones that define motion of a point object. The equation that is useful here is the following:

v² = u² + 2aS

u = 40 cm/s = 0.4 m/s; S = 7 cm = 0.07 m and g = 9.8m/s².

Hence,

v² = (0.4)² + 2(9.8)(0.07) = 0.16 + 1.372 = 1.532

Taking square root, v = 1.238 m/s = 123.8 m/s

b.

From equation of continuity,

A₁v₁ = A₂v₂

Using cgs units,

(40)(2) = (A₂)(123.8)

Solving, A₂ = 0.646 cm²