Question

The Prandtl number, Pr, is a dimensionless group important in heat transfer. It is defined as Pr = Cp*mu/k where Cp is the heat capacity of a fluid, mu is the fluid viscosity, and k is the fluid thermal conductivity. For a given fluid, Cp = 0.58 J/(g* deg C), k = 0.28 W/(m * deg C), and mu = 1934 Ibm / (ft * h). Determine the value of the Prandtl number for this fluid.

Answer 1

The value of the Prandlt number for this fluid is: 1656.04

Step-by-step explanation:

As it is stated in the problem : Pr = Cp*mu/k

where:

cp: heat capacity of the fluid

mu: viscosity of the fluid

k: thermal conductivity of the fluid

Now for a given fluid we have

cp= 0.58 J/(g* deg C)

mu=1934 Ibm / (ft * h)

k = 0.28 W/(m * deg C)

If we put these values in the ecuation of the Prandlt number we have:

Pr = (0.58 J/(g* deg C)) × (1934 Ibm / (ft * h) / 0.28 W/(m * deg C)) =

As we can see we have to convert the units so we can operate all the values in the same units of measurement and then cancel them so as to obtain a dimensionless result.

Converting the value of: mu = 1934 Ibm / (ft * h)

1 ft= 0.3048 m

1 h= 3600 s

1 lbm= 453.59 g

mu= 1934 Ibm / (ft * h) × (453,59 g/ lbm) × (1h/3600 s) × (1 ft/0.3048 m) = 799.47 g/ (m *s).

Pr = (0.58 J/(g* deg C)) × (799.47 g/ (m *s) / 0.28 W/(m * deg C)) = 1656.04