Page 31 - Modelling in Transport Phenomena A Conceptual Approach

12 CHAPTER 1. INTRODUCTION
PROBLEMS

1.1 One of your friends writes down the inventory rate equation for money as

of dollars ) = (Interest) - ( charge ) ( deposited )
Change in amount Service Dollars

- ( written )
Checks

Identify the terms in the above equation.

1.2 Determine whether steady- or unsteady-state conditions prevail for the
following cases:
a) The height of water in a dam during a heavy rain,
b) The weight of an athlete during a marathon,
c) The temperature of an ice cube as it melts.

1.3 What is the form of the function p(x, y) if a2p/ax&j = O?
(Answer: p(x, y) = f(z) + h(y) + C, where C is a constant)

1.4 Steam at a temperature of 200 "C flows through a pipe of 5 cm inside diameter
and 6cm outside diameter. The length of the pipe is 30m. If the steady rate of
heat loss per unit length of the pipe is 2W/m, calculate the heat fluxes at the
inner and outer surfaces of the pipe.
(Answer: 12.7 W/ m2 and 10.6 W/ m2)

1.5 Dust evolves at a rate of 0.3 kg/ h in a foundry which has the dimensions of
20 m x 8 m x 4 m. According to ILO (International Labor Organization) standards,
the dust concentration should not exceed 20 mg/ m3 to protect workers' health.
Determine the volumetric flow rate of ventilating air to meet the standards of ILO.
(Answer: 15,000 m3/ h)

1.6 An incompressible Newtonian fluid flows in the z-direction in space between
two parallel plates that are separated by a distance 2B as shown in Figure 1.3 (a).
The length and the width of each plate are L and W, respectively. The velocity
distribution under steady conditions is given by