Velocity upstream

AP = Line pressure drop, psi P], P2 = Upstream and downstream pressures in psi ABS S = Specific gravity of vapor relative to water = 0.00150 MP,/T d = Pipe diameter in inches Ui = Upstream velocity, ft/sec f = Friction factor (assume. 005 for approximate work)... 

U = upstream velocity, ft/sec f = friction factor (assume. 005 for approximate work)... 

K, to be used with upstream velocity head, Vf /2. (3 = d/D Contraction... 

As for the other obstruction meters, when the continuity equation is used to eliminate the upstream velocity from Eq. (10-11), the resulting expression for the mass flow rate through the orifice is... 

In both of these experimental arrangements, for a given mixture, there is a unique duct velocity (vu) that matches the burning velocity. In the Spalding burner, this is the adiabatic burning velocity (or the true, S U). If vu > Su the condition is not stable and the flame will blow off or move away from the exit of the duct until a reduced upstream velocity matches Su. If vu <, S U, the flame will propagate into the duct at a speed where the flame velocity is, S U vu. This phenomenon of upstream propagation is known as... 

Figure 11 Flow of a fiber suspension through a sudden expansion with an upstream velocity of 0.5 m/s (Heath et al., 2007) (see Plate 16 in Color Plate Section at the end of this book).

The determination of the surface shear stress t, from Eq, 6-9 is not practical since it requites a knowledge of the flow velocity profile. A more practical approach in external flow is to relate Tj to the upstream velocity V as... 

Consider laminar flow of a fluid over a flat plate, as shown in Hg. 6-29. Surfaces that are slightly contoured sucli as turbine blades can also be approximated as flat plates with reasonable accuracy. The jc-coordinaie is lueasured along the plate surface from the leading edge of the plate in the direction of the flow, and y is measured from the surface in the normal direction. The fluid approaches Ihe plate in the. r-direction with a uniform upstream velocity, which is equivalent to the free stream velocity V. 

The drag force Fq depends on the density p of the fluid, the upstream velocity V, and the size, shape, and orientation of the body, among other things. The drag characteristics of a body is represented by the dimensionless drag cocfilcient defmed as... 

Friction drag is a strong function of viscosity, and an idealized" fluid with zero viscosity would produce z.ero friction drag since the wall shear stress would be zero. The pressure drag would also be zero in this case during steady flow regardless of the shape of the body since there are no pressure losses. For flow in the horizontal direction, for example, the pressure along a horizontal line is constant (just like stationary fluids) since the upstream velocity is... 

The transition from laminar to turbulent flow depends on the surface geometry, surface roughness, upstream velocity, surface temperature, and the type of fluid, among other things, and is best characterized by the Reynolds number. The Reynolds number at a distance x from the leading edge of a flat plate... 

At very low upstream velocities (Re 1), the fluid contpletely wraps around the cylinder and the two arms of Ihe fluid meet on the rear side of the... 

C During flow over a given body, ihe drag force, the upstream velocity, and the fluid density are measured. Explain how you would deleimine the drag coefficient. What area would you use in calculations ... 

All velocities are divided by a reference velocity wa given for the problem, for example the upstream velocity of a body in crossflow. In the same way all lengths are divided by a reference length L given for the problem, an example of this is the length over which the fluid flows across a body. With this we can then form dimensionless quantities... 

COLOR FIGURE 3.3 Velocities in the wake region for a cylindrical vegetative canopy with a 5 m ground clearance immersed in a logarithmic upstream velocity profile with effective foliage element diameter = 0.001 m and a porosity of 0.99995. 

The definition of A" (i.e., Kj= 2efW) involves the kinetic energy of the fluid, V /2. For sections in which the flow area changes (e.g., pipe entrance, exit, expansion, contraction, etc.), the entering and leaving velocities will be different. Since the value of the velocity used with the definition of Kp is arbitrary, it is very important to know which velocity is implied when values of the loss coefQcient are used from various sources (e.g., handbooks, manuals, texts, etc.). In most cases it is the largest velocity, through the smallest flow area, but the values in Table 5.6 for contractions and expansions are all used with the upstream velocity. 

Rd = Reynolds number based on the pipe inner diameter and upstream velocity... 

Notice that the discharge coefficient, C, is a function of the upstream velocity in the pipe (W). Since the upstream velocity is not known, the solution to this equation requires an iterative procedure. 

Note that this value is based on the upstream velocity t). A different expression is obtained if the coefficient is based on Uj. 

Type in waves correspond to upstream velocities in the range aeio < go < afo... 

---