Importance:

• Mechanical energy balance calculations are useful for the following purposes in the furnace design:
• The motion of flue gases within the furnace chamber controls the rate of heat transfer and thermal gradients in the furnace
• Measurements of flow rates of fluid e. g. air and other liquids are required to control the process
• In certain physical processing like heat treatment, a gaseous atmosphere is maintained. Uniformity in the composition of the atmosphere is required to design the flow rates and rate of movement of the atmosphere.
  

Exercise -1
It is proposed to install a fan to draw air at rest in a horizontal straight duct of  cross section. The duct is 60 m long.

The air enters the duct at  measured at  and Calculate the horse power of the fan, if the fan discharges air at  pressure.

. Friction loss due to contraction and expansion are 0.4 and 1 respectively. Viscosity of 

SOLUTION
Applying mechanical energy balance between plane 1 and 2 and noting that  (duct is horizontal),  (inlet pressure at plane 1 = exit pressure at plane 2 and  (velocity at plane 1 = velocity at plane2), we get.

(1)

(2)

By 1 and 2 we get

(3)

F is friction factor and is a function of Reynold’s number.

(4)

                                                                                  
 and  

Inserting the values of  and  ( is velocity of air in duct), in eq. 4, we get
 

Flow is turbulent and we use

In the equation 3 substitute the values of  , to get.

 of fluid.


   
Now n heat recovery