Head loss calculation

The head losses calculated using K coefficients by these figures can be added directly to the total friction head loss for the straight pipe portions of a system. When equivalent lengths are determined, they must be added to the straight pipe before determining the total head loss, as shown in the example calculations for a water system. 

In addition to advanced hltration, this chapter also discusses carbon adsorption. This is a unit operation that uses the active sites in powdered, granular, and hbrous activated carbon to remove impurities from water and wastewater. Carbon adsorption and hltration share some similar characteristics. For example, head loss calculations and backwashing calculations are the same. Carbon adsorption will be discussed as the last part of this chapter. 

Head loss calculations for bed adsorption are therefore the same as those with filtration. Since head loss formulas through beds of solids have already been discussed under filtration, they will not be pursued here. The important point to remember is that for filtration formulas to apply under moving-bed adsorption operations, the superficial velocity should now be considered relative velocity. 

Qb and Qc are the outgoing flow rates through the two outlet apertures. Mass conservation dictates that Q = Qb+Qc- The fraction of the flow that passes through either outlet section is determined by a head loss calculation developed hereinafter. 

In order to select the pipe size, the pressure loss is calculated and velocity limitations are estabHshed. The most important equations for calculation of pressure drop for single-phase (Hquid or vapor) Newtonian fluids (viscosity independent of the rate of shear) are those for the deterrnination of the Reynolds number, and the head loss, (16—18). 

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 Pa gauge and 20 G through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90 elhows. Assume 0.5 velocity heads lost for the elhows. 

The calculation of the overall stage efficiency must also include losses encountered in the diffuser. Thus, the overall actual adiabatic head attained will be the actual adiabatic head of the impeller minus the head losses encountered in the diffuser from wake caused by the impeller blade the loss of part of the kinetic head at the exit of the diffuser (A(/ed), and the loss of head from frictional forces (A(/osf) encountered in the vaned or vaneless diffuser space... 

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

The certified flow resistance factor, K[, is a dimensionless factor used to calculate the velocity head loss that results from the... 

Equation 2-25 is valid for calculating the head loss due to valves and fittings for all conditions of flows laminar, transition, and turbulent [3], The K values are a related function of the pipe system component internal diameter and the velocity of flow for v-/2g. The values in the standard tables are developed using standard ANSI pipe, valves, and fittings dimensions for each schedule or class [3]. The K value is for the size/type of pipe, fitting, or valve and not for the fluid, regardless of whether it is liquid or gas/vapor. 

Alternate Calculation Basis for Piping System Friction Head Loss Liquids... 

In reciprocators hf is calculated at peak instantaneous flow, including maximum loss through a dirty filter, and an additional head loss to allow for pulsation acceleration is used ... 

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... 

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. 

To calculate —APf it is therefore necessary to evaluate e/d and obtain the corresponding value of

head loss due to friction hf as ... 

Figure 5-1 illustrates a method that will produce a system in which the parts fit together to accomplish the common goal of good control. Control valve share of total system flowing pressure drop will be 60% at normal flow. The system will still achieve maximum flow as long as the control valve trim selected can pass maximum flow at operating head loss (line 23 of Figure 5-1). The procedure described in Figure 5-1 is intended as a stand-alone device for guiding the calculations, and worksheets can be prepared from it.

Power input per unit mass of the system is equal to the rate of energy dissipation per unit mass of the liquid and it is estimated by considering the permanent pressure head loss across the orifice. The rate of energy dissipation due to eddy losses is the product of the head loss and the volumetric flow rate. Frictional pressure drop at downstream of the orifice can be calculated as,... 

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. 

If the frictional losses were expressed as the head loss, hf= APf/pg, then the quantity 4fLJdi would multiply u2/2g. Thus 4/Le/d, is the total number of velocity heads lost. Consequently, an alternative presentation of frictional losses for fittings is in terms of the number of velocity heads K lost for each fitting. In this case, the total frictional pressure drop may be calculated as... 

Although Pitot tubes are inexpensive and have negligible permanent head losses they are not widely used. They are highly sensitive to fouling, their required alignment is critical and they cannot measure volumetric flow rate Q or mean velocity u. The latter can be calculated from a single measurement only if the velocity distribution is known this can be found if the Pitot tube can be traversed across the flow. 

A liquid flows in a steady state in a cylindrical pipe of inside diameter d, = 0.05 m at a flow rate Q = 2 x 10 3 m3/s. Calculate the head loss and the pressure drop for a sudden expansion to a pipe of inside diameter 0.1 m, if the liquid density p — 1000 kg/m3. 

If liquid is flowing through the nozzle, shown in Fig. 11.6, at, say, 9 ft/s, the pressure at point D will be lower than that at point B. Assuming the velocity in the draw-off sump to be close to zero, we can calculate the pressure at point D as follows head loss due to increased velocity = 0.34X92 = 28 in of water. 

There are also many empirical formulas used for calculating the friction head loss in piping systems. These must be used carefully because many are based on the properties of specific fluids and are not applicable over a broad range of fluids, temperatures, and pressures. For example, the Hazen and Williams formula widely used for water flow ... 

The heights of head losses in Eq. (14-92) should be in consistent units, e.g., millimeters or inches of liquid under operating conditions on the tray As noted, hdc is calculated in terms of equivalent clear liquid. Actually the liquid in the downcomer is aerated and actual backup is... 

There are four fitting K factors in Eq. (6.11). Each of these factors represents a specific valve or pipe-fitting pressure head loss, fLID. Notice that this term is not a K term, but rather represents L, the actual straight length of pipe. The reason it is not a K term is that it represents a straight section of pipe. The/factor in Eq. (6.11), including the / factor in each of the K terms, is calculated using Eqs. (6.3), (6.4), or (6.5). Derivation of the K resistance coefficients is reviewed in the next section. 

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