Frictional Losses through Fittings and Valves: These losses are reported as resistance coefficient K, where K is the number of the velocity heads that is lost because of the fittings or an obstruction. These values are independent of friction factor. Fitting friction loss h_ff is given as

And sum of form friction loss and skin friction loss is designated as friction loss h_f given as

Bernoulli equation for incompressible fluid is:

which can be written as

Example 4.12: Calculate the height of the water in an open tank if water is delivered through a pipe having internal diameter of 0.5 in. The smooth brass pipe is 200 ft long. Water is discharged at a rate of 0.01 ft³/s to the atmosphere. The pipeline has an open globe valve (K_V = 6.9). Entrance and exit losses are given as K_ent = 0.78 and K_exit = 1.0. Use the following information:

Density of water = 62.37 lb/ft³; Viscosity of water = 7.53 ´ 10^-4 lb/(ft·s)

Solution:

C Cross-sectional area of the pipe, A = 0.00136 ft².

C Velocity of the fluid, V = 7.33 ft/s.

C Reynolds number, Re = 2.53 ´ 10⁴.

C Friction factor, f = 0.0061.

C Skin friction losses:

C Fittings and minor loss coefficient, K_f = 6.9 + 1.0 + 0.78 = 8.68

C Friction losses h_f:

C Apply Bernoulli equation (4.20)

Given Z₂ = w_e = 0, P₁ = P₂, V₁ = 0, V₂ = 7.33 ft/s, Z₁ is found to be 105.8 ft.