Chapter 3.9, Problem 30P

(A)

Interpretation Introduction

Interpretation:

The minimum pump work done to move 1 kg of water into tower

Concept Introduction:

The expression to calculate the height of the tower.

$V=\frac{\pi }{4}{D}^2\times H$

Here, height of tower is H, diameter of tower is D, and volume of the water in the tower is V.

The expression to calculate the work done.

$\begin{array}{c}W=F\times d\\ =ma\times d\end{array}$

Here, force is F, distance is d, mass is m, and acceleration is a.

(B)

Interpretation Introduction

Interpretation:

The minimum pump work done to move 1 kg of water into tower

Concept Introduction:

The expression to calculate the work done.

$\begin{array}{c}W=F\times d\\ =ma\times d\end{array}$

Here, force is F, distance is d, mass is m, and acceleration is a.

(C)

Interpretation Introduction

Interpretation:

The maximum velocity the water can have is

Concept Introduction:

The steady state energy balance equation for steam around the cylinder.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{v^2}{2}+gh\right)\right\}={\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{v_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{v_{out}^2}{2}+g{h}_{out}\right)+{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}$

Here, mass flow rate for inlet and outlet is ${\dot{m}}_{in}$ and ${\dot{m}}_{out}$, specific enthalpies of inlet and outlet is ${\widehat{H}}_i$ and ${\widehat{H}}_{out}$, heights at which streams enters and leave the system is $h_{in}$ and $h_{out}$, time taken is t, mass of the system is M, specific internal energy is $\widehat{U}$, velocity is v, height is h, acceleration due to gravity is g, rate at which work is added to the system is ${\dot{W}}_{EC}$, rate of shaft work is ${\dot{W}}_S$, and the rate of heat addition to the system is $\dot{Q}$.

(D)

Interpretation Introduction

Interpretation:

The maximum velocity the water can have is

Concept Introduction:

Write the steady state energy balance equation for steam around the cylinder.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{v^2}{2}+gh\right)\right\}={\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{v_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{v_{out}^2}{2}+g{h}_{out}\right)+{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}$

Here, mass flow rate for inlet and outlet is ${\dot{m}}_{in}$ and ${\dot{m}}_{out}$, specific enthalpies of inlet and outlet is ${\widehat{H}}_i$ and ${\widehat{H}}_{out}$, heights at which streams enters and leave the system is $h_{in}$ and $h_{out}$, time taken is t, mass of the system is M, specific internal energy is $\widehat{U}$, velocity is v, height is h, acceleration due to gravity is g, rate at which work is added to the system is ${\dot{W}}_{EC}$, rate of shaft work is ${\dot{W}}_S$, and the rate of heat addition to the system is $\dot{Q}$.