Elbows, friction losses

Elastoviscous behaviour 104 Elbows, friction losses in 91 Electrical analogue for unsteady heat transfer 397... 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

For determining the frictional head, refer to friction loss in pipes, bends, elbows and reducers and valves as provided in Tables A.I and A.2 ... 

Friction loss in bends, reducers, elbows etc. are provided in Table A.2 in equivalent pipe length. 

Determining the total friction loss, however, is not as simple. Friction loss is caused by a number of factors and all depend on the flow velocity generated by the pump. The major sources of friction loss include friction between the pumped liquid and the sidewalls of the pipe valves, elbows, and other mechanical flow restrictions or other flow restrictions, such as back-pressure created by the weight of liquid in the delivery storage tank or resistance within the system component that uses the pumped liquid. 

The frictional loss term F in Equation 4-28 represents the loss of mechanical energy resulting from friction and includes losses resulting from flow through lengths of pipe fittings such as valves, elbows, orifices and pipe entrances and exits. For each frictional device a loss term of the following form is used ... 

Frictional losses are evaluated separately for the air and the solid. To each of these, contributions are made by the line itself, the elbows and other fittings, and the receiving equipment. It is conservative to assume that the linear velocities of the air and solid are the same. Since the air flow normally is at a high Reynolds number, the friction factor may be taken constant at f, = 0.015. Accordingly the frictional power loss of the air is given by... 

The additional frictional losses due to pipeline fittings such as elbows may be added to the velocity head loss N = 4fL/DH using the same velocity head loss values as for incompressible flow. This works well for fittings which do not significantly reduce the channel cross-sectional area, but may cause large errors when the flow area is greatly... 

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 5 Pa gauge and 20°C through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90° elbows. Assume 0.5 velocity heads lost for the elbows. 

Methods of estimating friction losses for flow through straight pipes, orifices, nozzles, elbows, and so on are given in Section 10 of Perry s Chemical Engineers Handbook (see footnote 2) and will not be discussed in this text. In the balance of this book we consider only processes in which friction losses are either specified or neglected. 

Liquid Flow Measurement. The requirement of accurate liquid flow measurement can also elevate process equipment (see Figure 7-8). If liquid is near the boiling point, a static head is required in the front of the control valve to overcome pipe friction losses and avoid flashing in the line. Minimum equipment elevation, orifice range and minimum line size can be used if the orifice is as close to the equipment as possible and the piping has only one elbow up to the control valve. 

Pipes in a compressor circuit should connect directly point-to-point. Bends instead of elbows cause less friction loss and less vibration. Angular branch connections eliminate hard tees and give a smoother flow. Double offsets for a directional change should be avoided. Intercoolers closely integrated with the machine minimize piping. Pulsation dampeners should be located on the cylinders without any interconnecting pipe. Knockout drums should be adjacent to the machine. Several after-coolers or exchangers in the circuit should be stacked as much as possible for a direct gas flow. Equipment in the circuit should be in process flow sequence. 

So far all the discussion has been about steady flow well downstream of the pipe entrance in straight circular pipe. This is the simplest and one of the most important cases of fluid friction. However, in many fluid systems we must take into account the effect of valves, elbows, etc. They are much more complex to analyze than the one-dimensional flows we have considered so far. (The student is advised to take apart an ordinary household faucet and study its flow path it is much more complicated than that of a straight pipe.) Efforts have been made to calculate the friction losses in such fittings, and the results have been correlated in several convenient ways which allow us to treat them as if they were one-dimensional problems. 

The friction losses are associated with the flow in a 75 m length of 50 mm pipe including one gate valve, one globe valve, two short curvature elbows, a contraction (at A) and an expansion at B. At this stage, neglecting the contraction and expansion losses, one can express the loss term in terms of the unknown velocity V as ... 

This is the mechanical-energy loss due to skin friction for the pipe in N m/kg of fluid and is part of the F term for frictional losses in the mechanical-energy-balance equation (2.7-28). This term (Pi—Pz)/ for skin friction loss is different from the (p, — Pz) term, owing to velocity head or potential head changes in Eq. (2.7-28). That part of F which arises from friction within the channel itself by laminar or turbulent flow is discussed in Sections 2.10B and in 2. IOC. The part of friction loss due to fittings (valves, elbows, etc.), bends, and the like, which sometimes constitute a large part of the friction, is discussed in Section 2.10F. Note that if Eq. (2.7-28) is applied to steady flow in a straight, horizontal tube, we obtain (pi — Pz)/p = F. 

The Z f tsrm for frictional losses in the system includes the following (1) contraction loss at tank exit, (2) friction in the 4-in. straight pipe, (3) friction in 4-in. elbow, (4) contraction loss from 4-in. to 2-in. pipe, (5) friction in the 2-in. straight pif>e, and (6) friction in the two 2-in. elbows. Calculations... 

Momentum Balance on Reducing Elbow and Friction Losses. Water at 20°C is flowing through a reducing bend, where a2 (see Fig. 2.8-3) is 120°. The inlet pipe diameter is 1.829 m, the outlet is 1.219 m, and the flow rate is8.50 m /s. The exit point Z2 is 3.05 m above the inlet and the inlet pressure is 276 kPa gage. Friction losses are estimated as 0.5vjl2 and the mass of water in the... 

The additional pressure losses between (A) and (B) include the friction losses and pressure losses in all the pipe fittings such as valves, elbows, expansions, contraction branches, and bypasses. Pressure is also lost at entry and exit as well. Such pressure losses are expressed in terms of the Darcy-Weisbach equation and in terms of pressure loss factors for each fitting. 

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