Chapter 4, Problem 4.7P

(a)

Interpretation Introduction

Interpretation:

The pounds of salt present in the tank after 1 h 40 min is to be determined.

Concept Introduction:

The general continuity equation to be used for a controlled volume is:

  ${\displaystyle {\iint }_{C.S}\rho \left(v\cdot n\right)dA}+\frac{\partial }{\partial t}{\displaystyle {\iiint }_{C.V}\rho dV}=0$.... (1)

Here, C.S is the control surface over which the integral dA is taken, C.V is the control volume over which the integral dV is taken, $\rho$ is the density of the fluid, $v$ is the velocity vector, $n$ is the direction of the vector $v$ , The product $v\cdot n$ is scalar defined as:

  $v\cdot n=\left|v\right|\left|n\right|\cos \theta$

(b)

Interpretation Introduction

Interpretation:

The upper limit for the pounds of salt present in the tank if the process continue to infinity is to be determined.

Concept Introduction:

The general continuity equation to be used for a controlled volume is:

  ${\displaystyle {\iint }_{C.S}\rho \left(v\cdot n\right)dA}+\frac{\partial }{\partial t}{\displaystyle {\iiint }_{C.V}\rho dV}=0$.... (1)

Here, C.S is the control surface over which the integral dA is taken, C.V is the control volume over which the integral dV is taken, $\rho$ is the density of the fluid, $v$ is the velocity vector, $n$ is the direction of the vector $v$ , The product $v\cdot n$ is scalar defined as:

  $v\cdot n=\left|v\right|\left|n\right|\cos \theta$

(c)

Interpretation Introduction

Interpretation:

Thetime lapse if the quantity of salt in the tank is changed from 100 to 150 lb is to be determined.

Concept Introduction:

The general continuity equation to be used for a controlled volume is:

  ${\displaystyle {\iint }_{C.S}\rho \left(v\cdot n\right)dA}+\frac{\partial }{\partial t}{\displaystyle {\iiint }_{C.V}\rho dV}=0$.... (1)

Here, C.S is the control surface over which the integral dA is taken, C.V is the control volume over which the integral dV is taken, $\rho$ is the density of the fluid, $v$ is the velocity vector, $n$ is the direction of the vector $v$ , The product $v\cdot n$ is scalar defined as:

  $v\cdot n=\left|v\right|\left|n\right|\cos \theta$