Chapter 4, Problem 4.6P

(a)

Interpretation Introduction

Interpretation:

The average velocity of the fluid flowing through a circular duct of diameter 20 in. is to be calculated.

Concept Introduction:

Area ( A ) of a circle with diameterd is calculated as:

  $A=\frac{\pi d^2}{4}$.... (1)

Average velocity if a fluid flowing through a circular duct is calculated as:

  $v_{avg}=\frac{1}{\pi R^2}{\displaystyle {\iint }_{A}vdA}$.... (2)

Here, $R$ is the radius of the duct, $v$ is the velocity of the fluid in the duct, and $dA$ is the differential area of the duct.

(b)

Interpretation Introduction

Interpretation:

The flow rate of the fluid flowing through a circular duct of diameter 20 in. in cubic feet per second is to be calculated.

Concept Introduction:

Area ( A ) of a circle with diameterd is calculated as:

  $A=\frac{\pi d^2}{4}$.... (1)

Volumetric flowrate of a fluid flowing through a circular duct is calculated as:

  $\dot{V}={\displaystyle {\iint }_{A}vdA}$.... (3)

Here, $v$ is the velocity of the fluid in the duct, and $dA$ is the differential area of the duct.