Stagnation Pressure

Stagnation Pressure

• The stagnation pressure at a point in a fluid flow is the pressure which could result if the fluid were brought to rest isentropically.
  
• The word isentropically implies the sense that the entire kinetic energy of a fluid particle is utilized to increase its pressure only. This is possible only in a reversible adiabatic process known as isentropic process.

Fig 16.2   Measurement of Stagnation Pressure

• Let us consider the flow of fluid through a closed passage (Fig. 16.2). At Sec. l-l let the velocity and static pressure of the fluid be uniform. Consider a point A on that section just in front of which a right angled tube with one end facing the flow and the other end closed is placed.
  
• When equilibrium is attained, the fluid in the tube will be at rest, and the pressure at any point in the tube including the point B will be more than that at A where the flow velocity exists.
  
• By the application of Bernoulli’s equation between the points B and A, in consideration of the flow to be inviscid and incompressible, we have,

(16.6)

where p and V are the pressure and velocity respectively at the point A at Sec. I-I, and p₀ is the pressure at B which, according to the definition, refers to the stagnation pressure at point A.

• It is found from Eq. (16.6) that the stagnation pressure p₀ consists of two terms, the static pressure, p and the term ρV²/2 which is known as dynamic pressure. Therefore Eq. (16.6) can be written for a better understanding as

(16.7)

       

• Therefore, it appears from Eq.(16.7), that from a measurement of both static and stagnation pressure in a flowing fluid, the velocity of flow can be determined.
  
• But it is difficult to measure the stagnation pressure in practice for a real fluid due to friction. The pressure  in the stagnation tube indicated by any pressure measuring device (Fig. 16.2) will always be less than p₀, since a part of the kinetic energy will be converted into intermolecular energy due to fluid friction). This is taken care of by an empirical factor C in determining the velocity from Eq. (16.7) as

(16.8)