Velocity-head

Fig. 6. Illustration of variation of velocity of air at the oudet of a centrifugal fan and the function filled by several diameters of straight discharge duct in converting velocity head to static head and estabUshing normal turbulent dow distribution. Bends or obstmctions at the discharge oudet cause turbulence...

Pumping, Velocity Head, and Power. Mechanical mixers can be compared with pumps (1) because they produce circulating capacity and velocity head H. The analogy between a pump and mixer can be appreciated by comparing a pumping loop with a mixing tank (Fig. 2). Power input P to a pump is represented by... 

The velocity head JT in a pipe flow is related to Hquid velocity hy H = I Qc The Hquid velocity in a mixing tank is proportional to impeller tip speed 7zND. Therefore, JTin a mixing tank is proportional to The power consumed by a mixer can be obtained by multiplying and H and is given... 

The flow resistance of pipe fittings (elbows, tees, etc) and valves is expressed in terms of either an equivalent length of straight pipe or velocity head loss (head loss = Kv /2g ). Most handbooks and manufacturers pubHcations dealing with fluid flow incorporate either tables of equivalent lengths for fittings and valves or K values for velocity head loss. Inasmuch as the velocity in the equipment is generally much lower than in the pipe, a pressure loss equal to at least one velocity head occurs when the fluid is accelerated to the pipe velocity. 

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... 

In the velocity head method, the losses are reported as a number of velocity heads K. Then, the engineering Bernoulh equation for an incompressible fluid can be written... 

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. 

Trumpet-shaped enlargements for turbulent flow designed for constant decrease in velocity head per unit length were found by Gibson (ibid., p. 95) to give 20 to 60 percent less friclional loss than straight taper pipes of the same length. 

Type of fitting or valve Additional friction loss, equivalent no. of velocity heads, K... 

V = superficial velocity based upon the gross area of the screen K = velocity head loss... 

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

For commercial steel pipe, with a roughness of 0.046 mm, the friction factor for fully rough flow is about 0.0047, from Eq. (6-38) or Fig. 6-9. It remains to be verified that the Reynolds number is sufficiently large to assume fully rough flow. Assuming an abrupt entrance with 0.5 velocity heads lost,... 

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. 

Taper the diameter of the distributor pipe so that the pipe velocity and velocity head remain constant along the pipe, thus sud-stantially reducing pressure variation in the pipe. 

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). 

Readings given by open straight tubes (Fig. 10-ld and le are too low due to flow separation. Readings of closed tubes oriented perpendicularly to the axis of the stream and provided with side openings (Fig. 10-lg) may be low by as much as two velocity heads. 

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