A 1.0-cm-diameter pipe widens to 2.0, then narrows to 0.5. Liquid flows through the first segment at a speed of 4.0. What is the volume flow rate through the pipe?

3.14 * 10⁻⁴ m³ / s

Explanation:

The flow rate (Q) of a fluid is passing through different cross-sections remains of pipe always remains the same.

Q = Area x velocity

Given:

Diameters of 3 sections of the pipe are given as

d1 = 1.0 cm, d2 = 2.0 cm and d3 = 0.5 cm.

Speed in the first segment of the pipe is

v1 = 4 m/s.

From the equation of continuity the flow rate through different cross-sections remains the same.

Flow rate = Q = A1 v1 = A2 v2 = A3 v3.

Q = A1v1

=π/4 d²1 v1 = π/4 * 0.01² * 4.0 m³/s = 3.14 * 10⁻⁴ m³ / s