Friction, head loss Factor

Relative roughness, pipe, 132 Friction losses, 181 also see Chapter 2 Friction, head loss, 68 Compressible fluids, 101 Factor, 68 Vacuum lines, 131 Gas constants, R, 378 Gravity settlers, 228 Head, 180-200 Calculations, 183, 184, 185 Discharge, 180, 187 Friction, 183 Liquid, 183... 

Method for calculation of major losses of liquids. First determine fluid properties such as the density, and dynamic viscosity at the operating temperature. Determine the inner diameter of the pipe, and evaluate its absolute roughness based on Table 20.3. Then calculate the Reynolds number for average velocity of the liquid. Afterwards, either use the Moody chart to evaluate the Fanning friction factor based on the Reynolds number and relative roughness, or compute the Colebrook equation by successive iterations. Finally, use the Darcy-Weisbach equation to determine the friction head loss. 

Since the friction factor in a horizontal pipeline is related to the friction head loss, hf (units of length), by... 

The calculated results arc determined as follows. The Reynolds number is determined from the guessed velocity, the pipe diameter, the fluid density and viscosity. The friction factor is determined using Eq. (2.7). The Kf faaors for the elbows and valves are determined using Eq. (2.4). The Xf factors for the inlet and exit effects are determined using Eq. (2.6). The pipe Kf factor is found using Eq. (2.3). The excess head loss factors for the complete piping system are summed as shown. 

Water is pumped from a large reservoir to a point 65 ft higher than the reservoir. How many feet of head must be added by the pump if 8000 lb,yh flows through a 6 in. pipe and the frictional head loss is 2 ft The density of the fluid is 62.4 Ib ft and the pump efficiency is 60%. Assume the kinetic energy correction factor equals 1. 

Heat Exchanger Approach 5°C = 40°F Approx Friction Factor 0.005 (1 velocity head loss every 50-60 length to diameter ratios)... 

Equation 3.11 is due to Blasius(6) and the others are derived from considerations of velocity profile. In addition to the Moody friction factor / = 8R/pu2, the Fanning or Darcy friction factor / = 2R/pu2 is often used. It is extremely important therefore to be clear about the exact definition of the friction factor when using this term in calculating head losses due to friction. 

With the friction factors used by Moody and Fanning, / and / respectively, the head loss due to friction is obtained from the following equations ... 

For pipe fittings, valves, and other flow obstructions the traditional method has been to use an equivalent pipe length Lequiv in Equation 4-30. The problem with this method is that the specified length is coupled to the friction factor. An improved approach is to use the 2-K method,s-6 which uses the actual flow path length in Equation 4-30 — equivalent lengths are not used — and provides a more detailed approach for pipe fittings, inlets, and outlets. The 2-K method defines the excess head loss in terms of two constants, the Reynolds number and the pipe internal diameter ... 

The excess head loss terms 2 Kt are found using the 2-K method presented earlier in section 4-4. For most accidental discharges of gases the flow is fully developed turbulent flow. This means that for pipes the friction factor is independent of the Reynolds number and that for fittings Kf = and the solution is direct. 

Assume fully developed turbulent flow to determine the friction factor for the pipe and the excess head loss terms for the fittings and pipe entrances and exits. The Reynolds number can be calculated at the completion of the calculation to check this assumption. Sum the individual excess head loss terms to get 2 Kf. 

The simplified procedure with a direct solution can also be used. The excess head loss resulting from the pipe length is given by Equation 4-30. The friction factor/has already been determined ... 

In equation 1.14, z, P/(pg), and u2/(2ga) are the static, pressure and velocity heads respectively and hf is the head loss due to friction. The dimensionless velocity distribution factor a is for laminar flow and approximately 1 for turbulent flow. 

Now, the Darcy-Weisbach equation for head loss defines the friction factor,/ ... 

This can be converted to a velocity head loss, 4fL/D, assuming that the friction factor, 4f, is approximately equal to 0.02 for two-phase flow. It can then be added to the head loss for the two bends. 

The Moody chart for the friction factor for fully developed flow in circular pipes for use in the head loss relation -----. Friction factors in tlie turbulent flow... 

The difference between the theoretical and actual curves results primarily from circulatory flow. Other contributing factors to the head loss are fluid friction... 

Tables 2-9 and 2-10 present friction factor and head losses for water as a carrier fluid for plain and rubber-lined steel pipes. There is no point in tabulating other fluids here as they are rarely used for slurry mixtures.

AHf= head loss due to friction (in units of length) fp = Darcy-Weisbach friction factor Cl = constant... 

The friction loss for a closed channel and steady-state single-phase flow was examined in Chapter 2. Using the Darcy factor, the head loss for an open launder can be expressed in terms of the hydraulic radius ... 

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