Exercise -3

Apply mechanical energy balance equation to calculate velocity of gas flowing in a pipe
Velocity of gas flowing in a pipe is calculated by measuring the difference between the static pressure and the impact pressure by the pitot tube at a given point in the flow. The pitot tube consists of two openings: impact and static. Impact opening is directed to receive the impact of the flow and the static opening remains at parallel to the direction of flow.

Mechanical energy can be applied at plane 1 which is upstream from the impact point and plane 2 just at the impact point to find the relationship between pressure difference and velocity. Kinetic energy of the gas is converted to pressure at plane 2. At point 1 velocity is known and the pressure is that determined by static opening of pitot tube. At point 2 velocity is zero and pressure is that detected by impact opening.

Mechanical energy balance simplifies to 

(7)

(8)

The frictional losses are taken into account by the discharge coefficient which depends on the design of impact and static openings of the pitot tube. Thus eq. 8 becomes

(9)

                                                                          
Note that the pitot tube measures the pressure at a particular point in the flow and the velocity will also correspond to that point.  In order to obtain the complete velocity profile, it is necessary to traverse the pitot tube radially in order to be able to measure the pressure and then to calculate the velocity. The following relations can be used to calculate the average velocity: