To estimate the value of NPr without using a calculator, we can simplify the calculation by converting the given units to suitable units for the equation.
First, convert Cp from J/(goC) to J/(kgK) since the units for mass and temperature are more commonly used. We know that 1 goC is equal to 0.001 kgK, so:
Cp = 0.583 J/(goC) * 0.001 kgK/(1 goC) = 0.000583 J/(kgK)
Next, convert k from W/(moC) to W/(kgK) since we want the units of thermal conductivity to match the units of heat capacity. We know that 1 moC is equal to 0.001 kgK, so:
k = 0.286 W/(moC) * 0.001 kgK/(1 moC) = 0.000286 W/(kgK)
Finally, convert from lbm/(ft-h) to kg/(m s) since we want the units of viscosity to match the units of heat capacity and thermal conductivity. We know that 1 lbm is equal to 0.453592 kg, 1 ft is equal to 0.3048 m, and 1 h is equal to 3600 s, so:
= 1936 lbm/(ft-h) * 0.453592 kg/(1 lbm) * 1/(0.3048 m/1 ft) * 1/(3600 s/1 h) = 0.468176 kg/(m s)
Now we can calculate the dimensionless Prandtl number NPr:
NPr = Cp/k = (0.000583 J/(kgK))(0.468176 kg/(m s))/(0.000286 W/(kgK)) = 1.8934014
To determine the value of NPr with a calculator, we can use the given values directly in the equation:
NPr = (0.583 J/(goC))(1936 lbm/(ft-h))/(0.286 W/(moC)) ≈ 1.8934
Therefore, the value of NPr, using a calculator, is approximately 1.8934.
Expressing the answer in scientific notation with the correct number of significant figures, we get:
NPr ≈ 1.9 x 10^0
The Prandtl number, NPr, is a dimensionless group important in heat-transfer calculations. It is defined as Cp/k, where Cp is the heat capacity of a fluid, is the fluid viscosity, and k is the thermal conductivity. For a particular fluid, Cp = 0.583 J/(goC), k = 0.286 W/(moC), and = 1936 lbm/(ft-h). Estimate the value of NPr without using a calculator (remember, it is dimensionless), showing your calculations; then determine it with a calculator. Express your answer in scientific notation making sure it has the correct number of significant figures.
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