Hydraulic Calculations: Determining Headloss Due to Friction

How can we determine the headloss due to friction in a tubing?

Given the diameter, length, flowrate, hydraulic radius, and roughness coefficients.

Answer:

In hydraulic calculations for fluid flow through a pipe, the headloss due to friction is calculated using the given parameters.

The calculated area of the tube is 1.862 m^2 and the uniform flow section factor is 1.199 m^{5/3}. The headloss calculated by Manning's equation is 0.039m, while Hazen-Williams equation gives 0.058m.

Explanation:

The physical quantities involved in this problem are from fluid flow and hydraulic calculations and it is based on two widely used equations: the Manning's equation and the Hazen-Williams equation.

Let's first calculate the area (A) of the section of the tube. The tube is circular, with a diameter of 1.54m, hence the area is obtained using the formula for the area of a circle: A = πr^2 where r is the radius, half of the diameter. A = π * (1.54/2)^2 = 1.862 m^2.

Next, for the uniform flow section factor, AR^2/3, where R is the hydraulic radius (0.385m). Putting these values in: AR^2/3 = A * R^{2/3} = 1.862 * (0.385)^{2/3} = 1.199 m^{5/3}.

To calculate headloss, we will use both Manning's equation and Hazen-Williams equation.

Manning's equation is: hL = Q^n * L / (AR^{2/3}) where n is Manning's roughness coefficient (given as 0.0196), Q is the flowrate (2 m^3/s), L is the length of the tubing (366m). Using these values gives, hL_Manning = 0.039 m.

The Hazen-Williams equation is hL = 10.67 * Q^1.852 / (C^1.852 * D^4.87) where C is the roughness coefficient for Hazen-Williams equation (100) and D is the diameter of the tubing (1.54m). Putting in these values, we get headloss, hL_HazenWilliams = 0.058 m.

So, both methods give slightly different estimates for the frictional headloss in the tube.