The Prandtl number, Pr, is a dimensionless group important in heat transfer. It is defined as Pr = Cpmu/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.

Question

Chemistry

Jenna Lane

12 July, 07:14

The Prandtl number, Pr, is a dimensionless group important in heat transfer. It is defined as Pr = Cpmu/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.

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Yesenia Goodwin · Answer 1

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

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