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 ft^{3}/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/ft^{3};
Viscosity of water = 7.53 ´ 10^{-4}
lb/(ft·s)
Solution:
C
Cross-sectional area of the pipe, A = 0.00136 ft^{2}.
C
Velocity of the fluid, V = 7.33 ft/s.
C
Reynolds number, Re = 2.53 ´ 10^{4}.
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 Z_{2} = w_{e}
= 0, P_{1} = P_{2}, V_{1} = 0, V_{2}
= 7.33 ft/s, Z_{1} is found to be 105.8 ft.