Velocity head drop

The frictional effects of bends and fittings are often expressed in terms of a quantity called the velocity head drop . To introduce this concept, we begin by observing that the specific energy lost to friction, F(J/kg), for incompressible flow follows from an integration of the Fanning equation (4.20) with friction factor and velocity constant over the length of pipe ... 

Hence by comparing (7.35) with (7.33), it is clear that the valve velocity-head drop, K,., is given by... 

We may note that the pipe diameter and the valve diameter are by no means always the same indeed the requirement for good control often necessitates a valve size only 50% of the line diameter. Accordingly it is sensible to include a factor to make explicit allowance for this. At the same time, we may relate the velocity-head drop to the velocity-head drop at full-open by using equation (7.25), namely C = yCv Hence equation (7.36) may be rewritten ... 

D is the valve size (m), approximately equal to the diameter of the valve throat at fully open, and AT VO is the velocity head drop for the fully open valve when the pipe diameter is equal to the valve size ... 

FIgura 7.5 Velocity head drop across a fully open butterfly valve connected to a pipe with diameter equal to valve size. 

Velocity head drop across the 50 m of pipe before the valve follows from equation (4.46) as... 

The fact that the entrance is smoothly tapered allows us to put Kcon 0 (see Chapter 4, Section 4.10), but we need to add the velocity-head drop from the two right-angle bends, ATj, = 0.75 from Table 4.1, to produce the total velocity-head drop, K, between the upstream vessel and the valve Kut = + 2 x 0.75 = 5.1. 

Velocity head drop across the 10 m of pipe downstream of valve ... 

Now solve the equations listed in Section 6.4, except that the term 4 fL/D in equation (6.27) is replaced once more by AT7-, the equivalent form for velocity heads dropped ... 

Ktx and Kyy are the velocity-head drops associated with the frictional resistance in the pipes bringing in feed-streams X and Y,... 

By equation (4.43), the conductance. Cl, is related to the total velocity head drop, Kr, by ... 

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). 

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

The left term of Equation 2.80 represents a head drop required to accelerate the flow from an initial velocity to the final velocity V2. If the initial velocity is low it can be assumed negligible and if density p = I.A is substituted into Equation 2.80, it can be written as... 

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. 

If the maximum flow-rate required is 20,000 kg/h, calculate the pump motor rating (power) needed. Take the pump efficiency as 70 per cent and allow for a pressure drop of 0.5 bar across the control valve and a loss of 10 velocity heads across the orifice. 

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