Theory

The pressure loss in fluid flow (P_L) has two components: the friction loss (P_F) and the shock loss (P_X). Friction losses occur due to shear resistance between boundary wall of the duct and fluid flow as well as individual layers of viscous fluid. While shock losses are resulted mainly due to expansion and contraction of the duct, change in flow direction and presence of the obstruction in the flow path. Shock losses also occur at the inlet and outlet of system and at the junction of any air currents. Although friction loss constitutes major component of the pressure loss in a ventilation system, the shock losses may reach up to 30% of the total pressure loss (McPherson, year).

In presence of an obstruction in a fluid flow path, shock losses occur due to development of drag forces that acts in the direction opposite to the flow direction. Unlike frictional forces these losses are proportional to velocity.

There are two types of drag forces: form drag and friction drag

Form drag: These drag losses are due to the shape or formation of the object i.e. bodies with larger cross-section will have a higher drag loss than thin streamline bodies. Form drag losses follow the drag equation i.e. they are proportional to square of velocity.

Friction drag: These drag losses are associated with the interaction of object surface with fluid, and thus arises from the Van-der-wall or adhesive forces acting on it (Banerjee, 2003).

The mechanism of the formation of drag forces is explained in the different text books (Misra, 1985; Banerjee, 2003; Hartman et al., 1997; McPherson, 1993). A brief presentation referring to Banerjee (2003) is outlined here. In case, an object is immersed in a moving fluid, it experiences a drag force which tends to move the body longitudinally with the flow. A part of this force occurs due to friction drag caused by the sheer force of the moving fluid at the boundary of the obstruction; the other part of the drag force is due to the creation of unbalanced normal forces at the leading and the trailing ends of the obstruction and is called form drag or pressure drag. Figure 1 below explains the formation of drag forces around a cylindrical body immersed in a incompressible flow of real fluid. A thin boundary wall is created around the cylinder in zone of flow. Due to increase in the velocity on the side of the cylinder, the pressure will reduce continuously from point A to B. Thus a fluid element within the boundary layer experiences a net pressure force in the direction of the flow. This net pressure force overcomes the resisting sheer force and allows maintaining the motion of the element in the flow direction. The situation is different when an element of fluid within the boundary wall but beyond point B is considered. The fluid element now experiences a net pressure force in a direction opposite to its motion. It continues for some distance for its momentum, beyond which, the layer adjacent to the solid surface is brought to rest and separation of flow takes place. The boundary layer separation creates a relative low pressure region behind a body and this region is called wake. Thus for separated flow, there is a net imbalance of pressure which is the cause of form drag.

The drag forces developed depend upon the Reynolds Number (Re) and the geometry of obstruction. A dimensionless co-efficient, called, drag co-efficient is used to characterize the obstruction and flow condition pertaining to drag losses. The drag forces are found to vary with the frontal area of obstruction present in a fluid flow, velocity of the fluid and the density of the fluid. The drag force can be expressed by the following expression:

$$ \ Drag \ Force = S. C_D. \frac{\rho .v^2}{2} $$

Where, S = Frontal area of the body
C_D = Drag co-efficient
ρ = density of air
v = velocity of air

The drag force causes a static pressure loss (ΔP) in the air flow stream. If A is the area of the duct in which the obstruction is placed, (ΔP.A) must equal to the drag force. So, the equation becomes:

Kata thermometer can be used to estimate dry Kata cooling power as well as wet Kata cooling power. However, the dry-Kata reading gives an estimate of the heat loss from the surface of the bulb due to radiation, convection and hence it is of little importance, particularly under hot and humid conditions where most of the heat loss from the human body is through evaporation. So, the wet Kata cooling power is mostly used in practical cases. The wet Kata reading is obtained by covering the bulb of the Kata thermometer by wet muslin. The idea is to make it resemble the human body which loses heat by radiation, convection and evaporation.

The Wet Kata cooling power (K) is seen to be related with the wet-bulb temperature (T_W) and the air velocity (v). An empirical relationship between Kata cooling power with the wet bulb temperature and air velocity is cited in the mine ventilation book of Misra (1985). This empirical relationship is given below:

$$ S.C_D. \frac{\rho . v^2}{2} = \delta P . A $$ $$ \ Or \ , \delta P = C_D . \frac{S}{A} . \frac {\rho . v^2}{2} $$

Hence, the shock pressure due to presence of an obstruction can be experimentally determined by measuring shock pressure loss and the co-efficient of drag for particular obstruction geometry can be found out using above equation.

Apparatus Used:

• Measuring tape
• Differential Pressure Calculator (DPCalc)
• Throttling Devices (air regulator)
• Tubs filled with rock pieces (obstruction)
• Anemometer for air velocity measurement

Instruments

• Experimental duct set up
• Measuring tape
• Inclined tube manometer
• Vane anemometer
• Cardboard with a hole (air regulator)
• Cart filled with rock pieces (obstruction)