Pressure drop Velocity head

The upward flow of gas and Hquid in a pipe is subject to an interesting and potentially important instabiHty. As gas flow increases, Hquid holdup decreases and frictional losses rise. At low gas velocity the decrease in Hquid holdup and gravity head more than compensates for the increase in frictional losses. Thus an increase in gas velocity is accompanied by a decrease in pressure drop along the pipe, a potentially unstable situation if the flows of gas and Hquid are sensitive to the pressure drop in the pipe. Such a situation can arise in a thermosyphon reboiler, which depends on the difference in density between the Hquid and a Hquid—vapor mixture to produce circulation. The instabiHty is manifested as cycHc surging of the Hquid flow entering the boiler and of the vapor flow leaving it. 

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). 

Although it has been common practice to specify the pressure loss in ordinary valves in terms of either equivalent length of straight pipe of the same size or velocity head loss, it is becoming more common to specify flow rate and pressure drop characteristics in the same terms as has been the practice for valves designed specifically for control service, namely, in terms of the valve coefficient, C. The flow coefficient of a valve is defined as the volume of Hquid at a specified density that flows through the fully opened valve with a unit pressure drop, eg, = 1 when 3.79 L/min (1 gal /min) pass through the valve... 

Note that the total pressure drop consists of 0.5 velocity heads of frictional loss contrihiition, and 1 velocity head of velocity change contrihiition. The frictional contrihiition is a permanent loss of mechanical energy hy viscous dissipation. The acceleration contrihiition is reversible if the fluid were subsequently decelerated in a frictionless diffuser, a 4,000 Pa pressure rise would occur. 

Equation (6-95) is valid for incompressible flow. For compressible flows, see Benedict, Wyler, Dudek, and Gleed (J. E/ig. Power, 98, 327-334 [1976]). For an infinite expansion, A1/A2 = 0, Eq. (6-95) shows that the exit loss from a pipe is 1 velocity head. This result is easily deduced from the mechanic energy balance Eq. (6-90), noting that Pi =pg. This exit loss is due to the dissipation of the discharged jet there is no pressure drop at the exit. 

This equation shows that for 5 percent maldistribution, the pressure drop across the holes shoiild be about 10 times the pressure drop over the length of the pipe. For discharge manifolds with K = 0.5 in Eq. (6-147), and with 4/E/3D 1, the pressure drop across the holes should be 10 times the inlet velocity head, pV V2 for 5 percent maldistribution. This leads to a simple design equation. 

For return manifolds with K = 1.0 and 4fL/(3D) 1, 5 percent maldistribution is achieved when hole pressure drop is 20 times the pipe exit velocity head. 

Feed or withdraw from both ends, reducing the pipe flow velocity head and required hole pressure drop by a factor of 4. 

Here, V is the area average velocity, K is the number of velocity heads of pressure drop provided hy the uniform resistance, Ap = FCpV/2, and a is the velocity profile factor used in the mechanical energy bal-... 

For banks of in-line tubes,/for isothermal flow is obtained from Fig. 6-43. Average deviation from available data is on the order of 15 percent. For tube spacings greater than 3D(, the charts of Gram, Mackey, and Monroe (Trans. ASME, 80, 25—35 [1958]) can be used. As an approximation, the pressure drop can be taken as 0.32 velocity head (based on V ) per row of tubes (Lapple, et al.. Fluid and Paiiicle Mechanics, University of Delaware, Newark, 1954). 

Pressure drop due to hydrostatic head can be calculated from hquid holdup B.]. For nonfoaming dilute aqueous solutions, R] can be estimated from f i = 1/[1 + 2.5(V/E)(pi/pJ ]. Liquid holdup, which represents the ratio of liqmd-only velocity to actual hquid velocity, also appears to be the principal determinant of the convective coefficient in the boiling zone (Dengler, Sc.D. thesis, MIT, 1952). In other words, the convective coefficient is that calciilated from Eq. (5-50) by using the liquid-only velocity divided by in the Reynolds number. Nucleate boiling augments conveclive heat transfer, primarily when AT s are high and the convective coefficient is low [Chen, Ind Eng. Chem. Process Des. Dev., 5, 322 (1966)]. 

Knitted wire mesh serves as an effective entrainment separator when it cannot easily be foiiled by sohds in the liquor. The mesh is available in woven metal wire of most alloys and is installed as a blanket across the top of the evaporator (Fig. ll-122d) or in a monitor of reduced diameter atop the vapor head. These separators have low-pressure drops, usually on the order of 13 mm [ M in) of water, and collection efficiency is above 99.8 percent in the range of vapor velocities from 2.5 to 6 iti/s (8 to 20 ft/s) [Carpenter and Othmer, Am. nsi. Chem. 

Part Pressure Drop in Number of Velocity Heads Equation... 

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 ... 

If time permits and a more accurate estimate is desired, particularly if the compressor is intercooled or has sidestreams, the velocity head losses through the nozzles can be estimated using the values from Table 2-2. This is possible where the nozzle sizes are available or can readily be estimated. When coolers are involved, the drop through the cooler should be included. Subtract the pressure drop from the inlet pressure (of the stage following the element) and recalculate a modified pressure ratio for the section. The cooler pressure drop can be approximated by using 2 - i... 

In order to avoid the need to measure velocity head, the loop piping must be sized to have a velocity pressure less than 5% of the static pressure. Flow conditions at the required overload capacity should be checked for critical pressure drop to ensure that valves are adequately sized. For ease of control, the loop gas cooler is usually placed downstream of the discharge throttle valve. Care should be taken to check that choke flow will not occur in the cooler tubes. Another cause of concern is cooler heat capacity and/or cooling water approach temperature. A check of these items, especially with regard to expected ambient condi-... 

Conventionally, the pressure drop of a cyclone is expressed in terms of the fluid velocity head in the cyclone. If the head of the fluid velocity at the inlet of... 

A more sophisticated theory was given by Barth, in which the pressure drop of a cyclone is defined as a function of the swirling velocity head of the fluid in the outlet pipe as follows ... 

Pressure drop through the return ends of exchangers for any fluid is given as four velocity heads per tube pass ... 

To size the fan it is necessary to know the total air volume and the pressures in the system. These are calculated from the losses in the system on the longest or index leg, and begin with the hood. The hood entry loss can be expressed as 0.6 of the velocity head and is accurate enough for first estimates. The losses are then calculated on the velocities in the ducts. Each change of direction means a small loss in each length of duct. Added to the pressure drop loss across the collector and the outlet losses, these give the total static pressure required in the system. 

The pressure drop and the friction loss through a cyclone are most conveniently expressed in terms of the velocity head based on the immediate inlet area. The inlet velocity head, h i, which is expressed in inches of water, is related to the average inlet-gas velocity and density by ... 

Fev = Friction loss (inlet-velocity heads) A pev = Pressure drop through the cyclone (inlet-velocity heads)... 

The pressure drop over the shell nozzles should be added to this value although this is usually only significant with gases. In general, the nozzle pressure loss is 1.5 velocity heads for the inlet and 0.5 velocity heads for the outlet, based on the nozzle area or the... 

A velocity head is u2/2g, metres of the fluid, equivalent to (u2/2)p, N/m2. The total number of velocity heads lost due to all the fittings and valves is added to the pressure drop due to pipe friction. 

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