Pressure from frictional losses

This meter may thus be considered as an orifice meter with a variable aperture, and the formulae already derived are therefore applicable with only minor changes. Both in the orifice-type meter and in the rotameter the pressure drop arises from the conversion of pressure energy to kinetic energy and from frictional losses which are accounted for in the coefficient of discharge. The pressure difference over the float —AP. is given by ... 

The liquid head driving force of 16 ft, or 4 psi, shown in Fig. 10.4, is actually not all available to overcome the higher stripper pressure. The frictional loss of the piping used to feed the stripper should be subtracted from the liquid head driving force. In the jet fuel example presented above, this frictional loss was neglected. 

Note from Equation (4-20) that the larger the pressure drop (i.e., the smaller P) from frictional losses, the smaller the reaction rate ... 

Tube-side Pressure Drop. Friction loss inside tubes can be computed from the general formulations given in Chap. 13, but the losses caused by enlargements, contractions, and turns must be included in the calculations. In order to account for nonisothermal flow, Sieder and Tate recommend multiplying the friction loss calculated by isothermal formulations such as F.q. (13-1), p. 395, b the dimensionless ratio for turbulent... 

Pressure Drop. The pressure drop across a two-phase suspension is composed of various terms, such as static head, acceleration, and friction losses for both gas and soflds. For most dense fluid-bed appHcations, outside of entrance or exit regimes where the acceleration pressure drop is appreciable, the pressure drop simply results from the static head of soflds. Therefore, the weight of soflds ia the bed divided by the height of soflds gives the apparent density of the fluidized bed, ie... 

This is pressure drop (including friction loss) between run and branch, based on velocity in the mainstream before branching. Actual value depends on the flow split, ranging from 0.5 to 1.3 if mainstream enters run and from 0.7 to 1.5 if mainstream enters branch. 

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. 

Skin friction loss. Skin friction loss is the loss from the shear forces on the impeller wall caused by turbulent friction. This loss is determined by considering the flow as an equivalent circular cross section with a hydraulic diameter. The loss is then computed based on well-known pipe flow pressure loss equations. 

The basis for single-phase and some two-phase friction loss (pressure drop) for fluid flow follows the Darcy and Fanning concepts. The exact transition from laminar or dscous flow to the turbulent condition is variously identified as between a Reynolds number of 2000 and 4000. 

The theory of pressure losses can be established by developing Bernoulli s theorem for the case of a pipe in which the work done in overcoming frictional losses is derived from the pressure available. For a fluid flowing in a pipe, the pressure loss will depend on various parameters. If... 

Finally, the condensate is often pumped from the receiver to the boiler house. Pumped condensate lines carry only water, and rather higher water velocities can often be used to minimize pipe sizes. The extra friction losses entailed must not increase back pressures to the point where pump capacity is affected. Table 22.10 can be used to help estimate the frictional resistance presented by the pipe. 

The absolute pressure at the inlet to the pump is usually the atmospheric pressure in the receiver, plus the static head from the water surface to the pump inlet and minus the friction loss through the pipes, valves and fittings joining the pump to the receiver. If his absolute pressure exceeds the vapor pressure of water at the temperature at which it enters the pump, then a net positive suction hand (NPSH) exists. If this NPSH is above the value specified by the pump manufacturer, the water does not begin to boil as it enters the pump suction and cavitation is avoided. If the water entering the pump is at a higher temperature, its vapor pressure is increased and a greater hydrostatic head over the pump suction is needed to ensure that the necessary NPSH is obtained. 

Pressure drop on the tube-side of a shell and tube exchanger is made up of the friction loss in the tubes and losses due to sudden contractions and expansions and flow reversals experienced by the tube-side fluid. The friction loss may be estimated by the methods outlined in Section 3.4.3 from which the basic equation for isothermal flow is given by equation 3.18 which can be written as ... 

The pressure drop of a two-phase flow generally consists of three components frictional loss, momentum change, and elevation pressure drop arising from the effect of the gravitational force field. The local Ap therefore is normally written as... 

Example 5-5 The Toricelli Problem. Consider an open vessel with diameter Di containing a fluid at a depth h that is draining out of a hole of diameter D2 in the bottom of the tank. We would like to determine the velocity of the fluid flowing out of the hole in the bottom. As a first approximation, we neglect the friction loss in the tank and through the hole. Point 1 is taken at the surface of the fluid in the tank, and point 2 is taken at the exit from the hole, because the pressure is known to be atmospheric at both points. The velocity in the tank is related to that through the hole by the continuity equation... 

Example 5-6 Friction Loss in a Sudden Expansion. Figure 5-7 shows the flow in a sudden expansion from a small conduit to a larger one. We assume that the conditions upstream of the expansion (point 1) are known, as well as the areas A and A2. We desire to find the velocity and pressure downstream of the expansion (V2 and P2) and the loss coefficient, Kt. As before, V2 is determined from the mass balance (continuity equation) applied to the system (the fluid in the shaded area). Assuming constant density,... 

A special condition called slack flow can occur when the gravitational driving force exceeds the full pipe friction loss, such as when a liquid is being pumped up and down over hilly terrain. Consider the situation shown in Fig. 7-5, in which the pump upstream provides the driving force to move the liquid up the hill at a flow rate of Q. Since gravity works against the flow on the uphill side and aids the flow on the downhill side, the job of the pump is to get the fluid to the top of the hill. The minimum pressure is at point 2 at the top of the hill, and the flow rate (Q) is determined by the balance between the pump head (Hp = — w/g) and the frictional and gravitational resistance to flow on the uphill side (i.e., the Bernoulli equation applied from point 1 to point 2) ... 

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