Velocity Flow Meters – Pitot/Pitot-Static Tubes

Pitot tubes (also called pitot-static tubes) are an inexpensive and convenient way to measure  velocity  at  a  point  in  a  fluid.  They  are  used  widely  in  airflow measurements in ventilation and HVAC applications.  Definitions for three types of  pressures  or  pressure  measurements are  given  below.  Understanding these definitions aids in understanding the pitot tube equation.  Static pressure, dynamic pressure and total pressure are defined below and illustrated in Figure 5.

Static pressure is the fluid pressure relative to the surrounding atmospheric pressure. It is measured through a flat opening which is in parallel with the fluid flow as shown with the first U-tube manometer in Figure 5.

Stagnation pressure is the fluid pressure relative to the surrounding atmospheric pressure. It is measured through a flat opening which is perpendicular to and facing into the direction of fluid flow as shown with the second U-tube manometer in Figure 5. This is also called the total pressure.

Dynamic  pressure  is  the  fluid  pressure  relative  to  the  static  pressure.  It  is measured through a flat opening which is perpendicular to and facing into the direction of fluid flow as shown with the third U-tube manometer in Figure 5. This is also called the velocity pressure.

Figure 5. Various Pressure Measurements

Static pressure is typically represented by the symbol, p.   Dynamic pressure is equal to ½ ρV2.    Stagnation pressure, represented here by Pstag, is equal to static pressure plus dynamic pressure plus the pressure due to the height of the measuring point above some reference plane, as shown in the following equation.

Where the parameters are as follows: Pstag   =  stagnation pressure, lb/ft2

P     =  static  pressure, lb/ft2

ρ   =   density of fluid, slugs/ft3

γ  =   specific weight of fluid, lb/ft3

h  =  height above a specified reference plane, ft

V  =   average velocity of fluid, ft/sec

(V =  Q/A = volumetric flow rate/cross-sectional area normal to flow)

For pitot tube measurements, the reference plane can be taken at the height of the pitot tube measurement so that h = 0.   Then, stagnation pressure minus static pressure is equal to dynamic pressure:

The pressure difference, Pstag   -  P, can be measured directly with a pitot tube such as the third U-tube in Figure 5, or more simply with a pitot tube like the one shown in Figure 6, which has two concentric tubes.   The inner tube has a stagnation pressure opening and the outer tube has a static pressure opening parallel to the fluid flow direction.  The pressure difference is equal to the dynamic pressure (½ ρV2) and can be used to calculate the fluid velocity for known fluid density, ρ.

A consistent set of units is:  pressure in lb/ft2, density in slugs/ft3, and velocity in ft/sec.

For use with a pitot tube, Equation (8) will typically be used to calculate the velocity of the fluid. Setting (Pstag  – P)   =   ∆P, and solving for V results in the following equation:

In order to use Equation (9) to calculate fluid velocity from pitot tube measurements, it is necessary to obtain a value for the density of the flowing fluid at its temperature and pressure.  For a liquid, a value for density can typically be obtained from a table similar to Table 1 in this course.  Such tables are available in handbooks and fluid mechanics or thermodynamics textbooks. Pitot tubes are used more commonly to measure gas flow, for example, air flow in HVAC ducts. Density of a gas varies considerably with both temperature and pressure. A convenient way to obtain a value for density for a gas, at a known temperature and pressure, is through the use of the Ideal Gas Law.

The Ideal Gas Law, as used to calculate density of a gas, is as follows:

Where:        ρ  =  density of the gas at pressure, P, and temperature, T, slugs/ft3

MW = molecular weight of the gas, slugs/slug-mole (The average molecular weight typically used for air is 29.)

P =  absolute pressure of the gas, psia

T  =  absolute temperature of the gas, oR  (oF + 459.67 = oR) R =  Ideal Gas Law constant, 345.23 psia-ft3/slug-mole-oR

But, if this is the Ideal Gas Law, how can we use it to find the density of real gases?  Well, the Ideal Gas Law is a very good approximation for many real gases over a wide range of temperatures and pressures.  It does not work well for very high pressures or  very low temperatures (approaching the  critical  temperature and/or critical pressure for the gas), but for many practical situations, the Ideal Gas Law gives quite accurate values for the densities of gases.

Example #5: Estimate the density of air at 16 psia and 85 oF.

Solution: Convert 85 oF to oR:     85 oF =  85 + 459.67 oR  =  544.67 oR Substituting values for P, T, R, and MW into Equation 11 gives:

ρ  =  (29)[16/(345.23)(544.67)] =   0.002468 slugs/ft3