You have a swimming pool and are trying to determine the rate of evaporation of

Question

You have a swimming pool and are trying to determine the rate of evaporation of water

from the pool on a hot summer day. The pool is 7.5 m in diameter, the pool is 1.3 m

deep, and the water temperature is 18°C. At that temperature, the vapor pressure of water

is 0.021 bar. The average wind speed is 3 m/s and the air temperature and pressure is

29°C and 1 bar, respectively. The moisture content of the air is equal to a mole fraction

of 0.010. Under these conditions, the gas phase diffusion coefficient of water in air is

0.28 cm2/s. Use this information for problems 1-3 below.

1. Using the flux model of diffusion into a flowing stream (the model that had resulted

in the concentration profile being given by the error function):

a. What is the flux rate of water from the pool (mol/cm2-s)?

b. What is the evaporation rate of water from the pool (kg/hr)?

c. What is the effective mass transfer coefficient (m/s)?

d. What is the Sherwood number for the system?

e. What is the depth of the equivalent boundary layer (cm)?

2. Using the expression for convection associated with a fully developed laminar

boundary layer:

a. What is the Reynolds Number? Is the use of this correlation valid?

b. What is the Schmidt Number?

c. What is the Sherwood number for the system?

d. What is the effective mass transfer coefficient (m/s)?

e. What is the flux rate of water from the pool (mol/cm2-s)?

f. What is the evaporation rate of water from the pool (kg/hr)?

g. What is the depth of the equivalent boundary layer (cm)?

3. Assuming evaporation was controlled by natural convection instead of forced

convection or diffusion:

a. What is the Grashof Number?

b. Which is the appropriate correlation for this condition?

c. What is the Sherwood number for the system?

d. What is the effective mass transfer coefficient (m/s)?

e. What is the flux rate of water from the pool (mol/cm2-s)?

f. What is the evaporation rate of water from the pool (kg/hr)?

Explanation / Answer

Reynolds number formula is used in the problems to find the Velocity (V), density ( ), Viscosity ( ) and diameter (L) of the fluid. It is dimensionless. If 2000 < Re < 4000 it is called transition flow. The Kind of flow depends on value of Re

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