Question

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?

Answer 1

Answer:

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