Page 93 - Industrial Ventilation Design Guidebook

58 CHAPTER 4 PHYSICAL FUNDAMENTALS

The form of Eq. (4.56) depends on the chosen balance border. The border
can be chosen arbitrarily. When the balance space is chosen according to the
balance border 2, the energy equation is

Using the values corresponding to the states 1' and 2', hi is the resistance
height between V and 2', and p r and p 2> are determined by the pressure loss
and initial pressure. Other quantities are determined correspondingly. It is
worth noting that there are no outflow losses in this case. Generally, it is wise
to use energy balances in calculations.
The above is valid for a liquid flow, when the effect of compressibility
can be ignored when calculating gas flows with small pressure differences.
For instance, in ventilating duct work, air is not compressed, so the density
is considered as constant. In HVAC technology a unit of pressure fre-
quently used for convenience is a water column millimeter, 1 mm
H 2 O«10Pa.

4.1.5.5 Pressure Loss in Gas and Steam Pipes
When the gas compressibility no longer can be bypassed, the pressure loss
equation is written in a differential form

where dl is the differential pipe length and D is the diameter.
On the basis that pv m A = q m or v m= q m /pA,

When both sides of the equation are multiplied by p we have

For an ideal gas,

or when the gas follows the formula pv = h* /L,, where £ is the process factor
and h* = h -h Q, the deviation from the enthalpy of the reference state, Eq.
(4.60), can easily be integrated, giving

where p/p = constant.
If the pressures and densities are known we can solve for either q m or D
from this equation.