A cylindrical tube with three radially drilled orifices can be used as a flow di

Question

A cylindrical tube with three radially drilled orifices can be used as a flow direction indicator....

133. A cylindrical tube with three radially drilled orifices, as shown in Fig. P3.33, can be used as a flow-direction indicator. Whenever the pressure on the two side holes is equal, the pressure at the center hole is the stagnation pressure. The instrument is called a direction-finding Piot tube, or a cylindrical yaw probe. (a) If the orifices of a direction-finding Pitot tube were to be used to measure the free stream static pressure, where would they have to be located if we use our solution for flow around a cylinder? (b) For a direction-finding Pitot tube with orifices located as calculated in part (a), what is the sensitivity? Let the sensitivity be defined as the pressure change per unit angular change (ie·ip/ae). Figure P3.33

Explanation / Answer

(a)

The velocity at the surface of the cylinder is a function of (the angle) the local static pressure will also be a function of theeta. Once the pressure distribution has been defined, it can be used to determine the forces and the moments acting on the configuration.

Using the Bernoulli's equation [given below]

P + (1/2)XXU2 = constrant -------(1)

P - Pressure of the liquid

- Density of the liquid

U - Velocity of the liquid

Expressure for the dimensional, local - static pressure distribution using eq. (1)

P = Pinfinity + (1/2)infinityXU2infinity - 2Uinfinity sin2 ---(2)

(b)

Sensitivity = (change in pressure) / change in angle

Sensitivity = dP / d

Here ro (liquid density) is a constant

Differenciate eq.(2) with respect to (theeta)

dP/d = [d(Pinfinity) / d] + [(1/2)infinity2UdUinfinity/d] - 2(dUinfinity/d)sin2+ 2Uinfinity2sincos ----(3)

Eq.3. represents the sensitivity of the pitot tube

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