Pressure drop in pipes

Normally, the pressure drop for gases flowing through pipes without packing ctui be neglected. For flow in pipes, the pressure drop along the length of the pipe can be approximated by 

For the flow conditions given in Example 5-4 in a 1000-ft length of IK-inch schedule 40 pipe (Op == 0.0118 fr ), the pressure drop is less than 10%. However, for high volumetric flow rates through microreactons, the pressure drop could be significant. 

Plot the pressure drop in a 60 ft length of iK-inch schedule 40 pipe packed with catalyst pellets K -inch in diameter. There is 104.4 lb,n/h of gas passing through the bed. The temperature is constant along the length of pipe at 26ff C. The void fraction is 45% and the properties of the gas are similar to tho.se of air at this temperature. The entering pressure is 10 atm. 

Substituting these values into Equation (S-251 gives 

Wc note that the turbulent flow term. Term 2. is dominant. 

The friction factor is a function of the Reynolds number and pipe roughness. The mass velocity, G. is constant along the length of the pipe. Replacing u with G/p, and combining with Equation (4-23) for the case of constant temperature, T, and total molar flow rate. Fj, Equation (4-35) becomes 

Integrating with limits P - Pf when Z. = 0, and assuming that / does not vary, we have 

Neglecting the second term on the right-hand side gives upon rearrangement 

Plot the pressure drop in a 60 ft length of 1 i -in. schedule 40 pipe packed with cat-alyst pellets i-in. in diameter. There is 104.4 Ib/h of gas passing through the bed. 

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Fig. 1. Effect of energy use on total cost where total cost is the sum of capital and energy costs for the lifetime of the plant, discounted to present value. Point D corresponds to the design point if the designer uses an energy price that is low by a factor of four in projected energy price. Effects on costs of (a) pressure drop in piping, (b) pressure drop in exchangers, (c) heat loss through insulation, (d) reflux use, and (e) energy recovery through waste-heat boiler...

When a fluid flows over a stationary or moving surface, the pressure of the fluid decreases along the length of the surface due to friction. This is commonly called the pressure drop of the system. Of particular interest are the pressure drops in pipes (tubes) and in heat exchanger shells. 

While the modified energy equation provides for calculation of the flowrates and pressure drops in piping systems, the impulse-momenlum equation is required in order to calculate the reaction forces on curved pipe sections. I he impulse-momentum equation relates the force acting on the solid boundary to the change in fluid momentum. Because force and momentum are both vector quantities, it is most convenient to write the equations in terms of the scalar components in the three orthogonal directions. 

Euler number Neu. . A P Neu PV2 AP = pressure drop in pipe (Pressure energy)/ (kinetic energy) Flow in closed conduits... 

In any real situation, reactants only flow through the reactor because there is a difference in pressure between the inlet and the outlet. Methods for calculating the pressure drop in pipes and packed beds have been outlined in Chap. 1. Often, the pressure drop is negligible compared with the total pressure and it is usual to assume that a tubular reactor with plug flow operates at constant pressure. 

Compute the size of the connection pipe. In usual vacuum-pump practice, the pressure drop in pipes serving mechanical pumps is not allowed to exceed 20 percent of the inlet pressure prevailing under steady operating conditions. A correctly designed vacuum system, where this pressure loss is not exceeded, will have a pump-down time which closely approximates that obtained under ideal conditions. 

There are many well-known dimensionless groups that are used in transport phenomena. Earlier, the Reynolds number was used to correlate data on pressure drop in pipe flow. For correlating data on heat transfer, often the dimensionless groups Nus-selt (Nu), Reynolds (Re), Prandtl (Pr), and Grashof (Gr) are used. They are defined as ... 

SUCTION LINE LOSSES (PRESSURE DROP IN PIPING), psi. SUCTION STATIC HEAD OF LIQUID ON PUMP SUCTION OR DISCHARGE, ft. 

Because of their commercial importance, data related to the handling of foods are very useful. For information related to the practice of chemical engineering, such as pressure drop in pipe flow, the reader is referred to studies by Metzner (22) and others (2, 21) Here studies conducted specifically with foods are considered. 

The analogy between heat and momentum does not account for the pressure drop in pipes and is not, strictly speaking, valid for pipe flow. However, the effect of pressure drop on this analogy appears to remain within the uncertainty of the available experimental data and is usually ignored. Next, introducing Eq. (6.16) into Eq. (5.63) gives the heat transfer in fully developed turbulent flow over a flat plate,... 

Problem 9.6 A mixture of O2/CO2 (stream 1) expands in turbine (see Figure Q-4b The outlet (stream 2) is mixed with a stream of pure oxygen and the new stream (number 4) passes through a heat exchanger and exits as stream 5. The efficiency of the turbine is 80%. There are no heat losses and pressure drops in pipes and in the heat exchanger can be ignored. 

In summary, even though the characteristic length scales of turbulent flows in microchannels are several orders of magnitudes smaller than their counterparts in macroscale pipes and channels, experimental evidence suggests the flows are statistically and structurally similar. As such, long established correlations for pressure drop in pipes and channels and computational tools available for the study of turbulent pipe and chaimel flows should be equally applicable to turbulent microchannel flows. 

Liquid viscosity data are needed for the design of fluid transport and mixing processes (e.g., pumps, pressure drops in pipes or pipelines, and stirred vessels) and have a significant influence on the effectiveness of heat exchangers and diffusion processes. The required accuracy for viscosity calculations is lower than for thermodynamic properties, but the correct order of magnitude must be met. 

Mackay, M. E., Y. L. Yeow and D. V. Boger, Pressure Drop in Pipe Contractions—Experimental Measurements or Finite Element Simulation , Chem. Eng. Res. Des. 66 22-25 (1988). 

The most commonly used analytical expressions relating flow rate with pressure drop in pipes, for power law fluids, are as follows. Under laminar flow conditions ... 

In all of our Case studies and in chemical engineering generally, pressure drop in pipe lines and across items of equipment is important. Power has to be supplied to overcome the viscous forces at the walls of the pipes. Thus the key element is the shear stress at the wall T(). The retarding viscous force is where L is the pipe length,... 

Noting that power = volumetric flow rate x pressure drop, the overall power per unit mass of liquid is straightforward to calculate for single-phase systems given the friction factors and voidage fraction in the mixer as supplied by mixer manufacturers or measured in the laboratory. For gas-liquid systems the volume of fluid in the mixer must be multiplied by (1 — c )) to obtain the liquid volume, so the gas fraction 4) must be known (see Section 11-5). It has been found that the Lockhart-Martinelli (1944) correction for the effect of the gas phase on pressure drop in pipe flow can be applied to static mixers with reasonable accuracy ( 20%). 

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