Friction losses, 181 also

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... 

Friction losses also occur due to turbulence caused by branch entries, elbows and contractions and expansions in duct diameter. For example, when the diameter of a duct is contracted, the static pressure in the larger diameter duct... 

From equation 60 one can obtain a theoretical power requirement of about 900 kWh/SWU for uranium isotope separation assuming a reasonable operating temperature. A comparison of this number with the specific power requirements of the United States (2433 kWh/SWU) or Eurodif plants (2538 kWh/SWU) indicates that real gaseous diffusion plants have an efficiency of about 37%. This represents not only the barrier efficiency, the value of which has not been reported, but also electrical distribution losses, motor and compressor efficiencies, and frictional losses in the process gas flow. 

In a submerged-tube FC evaporator, all heat is imparted as sensible heat, resulting in a temperature rise of the circulating hquor that reduces the overall temperature difference available for heat transfer. Temperature rise, tube proportions, tube velocity, and head requirements on the circulating pump all influence the selec tion of circulation rate. Head requirements are frequently difficult to estimate since they consist not only of the usual friction, entrance and contraction, and elevation losses when the return to the flash chamber is above the liquid level but also of increased friction losses due to flashing in the return line and vortex losses in the flash chamber. Circulation is sometimes limited by vapor in the pump suction hne. This may be drawn in as a result of inadequate vapor-liquid separation or may come from vortices near the pump suction connection to the body or may be formed in the line itself by short circuiting from heater outlet to pump inlet of liquor that has not flashed completely to equilibrium at the pressure in the vapor head. 

The economics would depend upon the smoother flow of fluid without exce.ssive friction loss. A smaller section of pipe may not only require a higher h.p. for the same suction and lifting head due to greater frictional losses, but may also cause the pipe to deteriorate quickly as a result of the additional load on its surface. Losses due to bends ami valves should also be added in the total friction loss. 

Calculate individual totalpressurelossefi for duct, elbows, expansions, etc. For fittings, the losses are total when calculated as indicated by the equations, and the duct loss is friction only. Also see references 11 and 128 and Chapter 2, V. 1, 3 Ed., of this series. 

The property of a fluid that resists any force such as atmospheric or pump pressure, tending to produce flow. Viscosity is a function of the fluids cohesive forces and generally decreases with increase in temperature. Also, friction losses decrease with increase in temperature. 

The work done in a reversible compression will be considered first because this refers to the ideal condition for which the work of compression is a minimum a reversible compression would have to be carried out at an infinitesimal rate and therefore is not relevant in practice. The actual work done will be greater than that calculated, not only because of irreversibility, but also because of frictional loss and leakage in the compressor. These two factors are difficult to separate and will therefore be allowed for in the overall efficiency of the machine. 

Equation (6-35) is also known as the von Karman-Nikuradse equation and agrees well with observations for friction loss in smooth pipe over the range 5 x 103 < NRe < 5 x 106. 

All the relationships presented in Chapter 6 apply directly to circular pipe. However, many of these results can also, with appropriate modification, be applied to conduits with noncircular cross sections. It should be recalled that the derivation of the momentum equation for uniform flow in a tube [e.g., Eq. (5-44)] involved no assumption about the shape of the tube cross section. The result is that the friction loss is a function of a geometric parameter called the hydraulic diameter ... 

Piping systems often involve interconnected segments in various combinations of series and/or parallel arrangements. The principles required to analyze such systems are the same as those have used for other systems, e.g., the conservation of mass (continuity) and energy (Bernoulli) equations. For each pipe junction or node in the network, continuity tells us that the sum of all the flow rates into the node must equal the sum of all the flow rates out of the node. Also, the total driving force (pressure drop plus gravity head loss, plus pump head) between any two nodes is related to the flow rate and friction loss by the Bernoulli equation applied between the two nodes. 

The adiabatic condition occurs, for example, when the residence time of the fluid is short as for flow through a short pipe, valve, orifice, etc. and/or for well-insulated boundaries. When friction loss is small, the system can also be described as locally isentropic. It can readily be shown that an ideal gas under isentropic conditions obeys the relationship... 

The pitot tube is a relatively complex device and requires considerable effort and time to obtain an adequate number of velocity data points and to integrate these over the cross section to determine the total flow rate. On the other hand the probe offers minimal resistance to the flow and hence is very efficient from the standpoint that it results in negligible friction loss in the conduit. It is also the only practical means for determining the flow rate in very large conduits such as smokestacks. There are standardized methods for applying this method to determine the total amount of material emitted through a stack, for example. 

Because the discharge coefficient accounts for the non-idealities in the system (such as the friction loss), one would expect it to decrease with increasing Reynolds number, which is contrary to the trend in Fig. 10-4. Flowever, the coefficient also accounts for deviation from plug flow, which is greater at lower Reynolds numbers. In any event, the coefficient is not greatly different from 1.0, having a value of about 0.985 for (pipe) Reynolds numbers above about 2 x 105, which indicates that these non-idealities are small. 

Pumps are devices for supplying energy or head to a flowing liquid in order to overcome head losses due to friction and also, if necessary, to raise the liquid to a higher level. The head imparted to a flowing liquid by a pump is known as the total head Ah. If a pump is placed between points 1 and 2 in a pipeline, the heads for steady flow are related by equation 1.14... 

For a given F, the height of hquid in the tank at steadystate would also be some constant h. The value of k would be that height that provides enough liy drau-lic pressure head at the inlet of the pipe to overcome the frictional losses of liquid flowing down the pipe. The higher the flow rate F, the higher h will be. 

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