Problem 5.3.5

Water is flowing through a pipe having 1.5-inch OD (outer diameter), 16 BWG (Birmingham wire gauge) corresponding to an ID (internal diameter) of 1.37 inch. Water is to be heated from 80 degrees Fahrenheit to final temperature of 120 degrees Fahrenheit.

Find out the values of Nusselt number for the following cases:

1. Water flowing at 200 pounds per hour with a pipe length of 10 feet.
2. Water flowing at 200 pounds per hour with a pipe length of 5 feet.
3. Water flowing at 800 pounds per hour with a pipe length of 10 feet.
4. Water flowing at 2,000 pounds per hour with a pipe length of 10 feet.

Viscosity of water wall temperature is reported a s1.406 pound per foot per hour

Solution:

(See Problem 5.3.1 also). Bulk temperature of water is 80 plus 120 over 2 equals 100 degrees Fahrenheit. So properties of water at this temperature can be seen as specific heat 0.998 BTU per pound per degree Fahrenheit, density 62.0 pounds per cubic foot, viscosity 1.65 pounds per foot per hour, thermal conductivity 0.363 BTU per hour per foot per degree Fahrenheit. Further, viscosity correction factor, phi, is 1.0227.

Cross sectional area of the pipe, A, is pi over 4 d squared is 0.0102 square feet. Velocity of water can be calculated by using the value of mass flow rate, and dividing it by density, giving us volumetric flow rate, and then dividing it by area. Now we can find Reynolds number by multiplying V by d time rho by mu.

Prandtl number would be calculated by multiplying c by mu and dividing it by k. Its value is equal to 4.56. And Graetz number, another dimensionless number, would be a product of Reynolds, Prandtl and d over L.

For Case 1, Velocity could be found to be 315.12 feet per hour. Reynolds number is 1,352, which is less than 2,100. Graetz number is 70.01, less than 100. With Reynolds number less than 2,100 and Gratez number less than 100, the appropriate correlation is

Nusselt number is 3.66 plus 0.085 times Graetz number over (one plus 0.047 times Gratez) times phi. Plugging in their values, Nusselt number is 5.08.

For Case 2, Velocity is again 315.12 feet per hour. Reynolds number is 1,352, but Graetz number is 140.02, greater than 100. The appropriate correlation is

Nusselt number is 1.86 times Graetz number to the power 0.333 times phi. Nusselt number is found to be 9.86.

For Case 3, Velocity is found to be 1,260.5.12 feet per hour. Reynolds number is 5,407, which is greater than 2,100 but less than 10,000. Graetz number is 280.04, greater than 100. The appropriate correlation is given as a function Reynolds number, Prandtl number, and other factors. Plugging in their values, Nusselt number is 37.39.

For Case 4, Velocity is found to be 3,151 feet per hour. Reynolds number is 13,520, which is greater than 10,000. Graetz number is 700.11. The appropriate correlation is 0.023 times Reynolds number raised to the power 0.8 times Prandtl number raised to the power 0.333. Plugging in their values, Nusselt number is 78.5.