Chapter 4, Problem 4.3P

Interpretation Introduction

Interpretation:The value of the average velocity in 1.5ft pipe should be calculated.

Concept introduction:Law of conservation of mass: It states that energy can neither be created nor be destroyed. The generalized form of an equation is written as:

[Rate of mass in from control volume] - [Rate of mass out from control volume] + [Rate of accumulation]

Equation of integrated mass balance over control volume,

  ${\displaystyle {\iint }_{c,s}\text{ρ}\left(\overrightarrow{v}\cdot \overrightarrow{n}\right)}\text{dA+}\frac{\text{d}}{\text{dt}}{\displaystyle {\iiint }_{c,V}\text{ρdV}}$

Where,

  $\overrightarrow{v}$ is the velocity vector.

  $\overrightarrow{n}$ is the normal vector

  $\text{ρ}$ is the density

  dA is the small element of the area on the control surface.

  dV is the control volume.