Page 87 - Industrial Ventilation Design Guidebook

5 2 CHAPTER 4 PHYSICAL FUNDAMENTALS

FIGURE 4.2 Tube flow velocity profile.

or

where
v m is mean velocity (velocity is zero at the surface)
/is a dimensionless friction factor
£ = 4/; this is the Blasius friction factor
In some literature A or j3 is used instead of £; it is essential to use £, be-
cause A is used for thermal conductivity and ft is used for cubic expansion of
air or an angle.
In a tube, the pressure is constant in all radial directions perpendicular to
the axis; it varies only in the flow direction x. The power balance of the ele-
r
m*3>nt- /"/A" /"i ja*ij"kt"i in nr f-Kio. c**/^f*i/ An<i 1 cnfTi/-*<=» '3t**»a oo A <in/i t-K** r\£*f tt"*ri&r\T *3O i nrnr^c

Denoting the hydraulic diameter as d h = 4A / C, we have

and the friction resistance head corresponding to the pressure difference is

The factor £ depends on the Reynolds number, which is a dimensionless vari-
able that denotes the nature of flow:

where
v m is the mean velocity
d is the characteristic length of a surface; in the case of flow in a tube it is the
tube diameter (note that d may be expressed by L in the case of a plate)
v is the kinematic viscosity
17 is the dynamic viscosity
q m in the mass flow