Chapter 4, Problem 4.3P

(a)

Interpretation Introduction

Interpretation:

The initial flowrate of water from the tank is to be calculated.

Concept Introduction:

The Bernoulli equation without friction is:

  $\frac{p_a}{\rho }+\frac{g{Z}_a}{g_c}+\frac{u_a^2}{2g_c}=\frac{p_b}{\rho }+\frac{g{Z}_b}{g_c}+\frac{u_b^2}{2g_c}$ ...... (1)

Here, $p_a\text{ and }{p}_b$ are the pressures at points a and b of the tube. $Z_a\text{ and }{Z}_b$ are the height of the tube at points a and b , $u_a\text{ and }{u}_b$ are the liquid velocity at points a and b of the tube, $\rho$ is the density of the fluid and $g$ is the acceleration due to gravity.

(b)

Interpretation Introduction

Interpretation:

Time required for the tank to empty is to be calculated.

Concept Introduction:

The Bernoulli equation without friction is:

  $\frac{p_a}{\rho }+\frac{g{Z}_a}{g_c}+\frac{u_a^2}{2g_c}=\frac{p_b}{\rho }+\frac{g{Z}_b}{g_c}+\frac{u_b^2}{2g_c}$ ...... (1)

Here, $p_a\text{ and }{p}_b$ are the pressures at points a and b of the tube. $Z_a\text{ and }{Z}_b$ are the height of the tube at points a and b , $u_a\text{ and }{u}_b$ are the liquid velocity at points a and b of the tube, $\rho$ is the density of the fluid and $g$ is the acceleration due to gravity.

Volume of a cylinder having height h and diameter d is calculated as:

  $V=\frac{\pi d^{2}h}{4}$ ...... (2)

(c)

Interpretation Introduction

Interpretation:

The average flowrate is to be calculated and compared with the initial flowrate of water.

Concept Introduction:

The Bernoulli equation without friction is:

  $\frac{p_a}{\rho }+\frac{g{Z}_a}{g_c}+\frac{u_a^2}{2g_c}=\frac{p_b}{\rho }+\frac{g{Z}_b}{g_c}+\frac{u_b^2}{2g_c}$ ...... (1)

Here, $p_a\text{ and }{p}_b$ are the pressures at points a and b of the tube. $Z_a\text{ and }{Z}_b$ are the height of the tube at points a and b , $u_a\text{ and }{u}_b$ are the liquid velocity at points a and b of the tube, $\rho$ is the density of the fluid and $g$ is the acceleration due to gravity.

Volume of a cylinder having height h and diameter d is calculated as:

  $V=\frac{\pi d^{2}h}{4}$ ...... (2)