Question

A stream moving with a speed of 0.9 m/s reaches a point where the cross-sectional area of the stream decreases to one-third of the original area. What is the water speed in this narrowed portion of the stream

Answer 1

Answer:

The water speed in this narrowed portion of the stream is 2.7 m/s.

Explanation:

Given;

initial speed of the stream, v₁ = 0.9 m/s

let the initial area of the stream, = A₁

then, the final area of the stream, A₂ = ¹/₃A₁

final speed of the water, v₂ = ?

Apply continuity equation;

A₁v₁ = A₂v₂

$v_2 = \frac{A_1v_1}{A_2}\\\\v_2 = \frac{A_1(0.9)}{A_1/3}\\\\v_2 = \frac{3A_1(0.9)}{A_1}\\\\v_2 = 3(0.9)\\\\v_2 = 2.7 \ m/s$

Therefore, the water speed in this narrowed portion of the stream is 2.7 m/s.