FLUID MECHANICS - THEORY

Velocity at a Point using a Pitot Tube

fig. 1 Piezometer and Pitot Tube

fig. 2 Stagnation Point

A combination of piezometer and pitot tube can be used to obtain the velocity at a specific point. Static pressure can be measured using a piezometer. The Pitot tube, as shown in the figure, can be used to measure the stagnation pressure. Stagnation pressure is the pressure when the flow has a stagnation velocity (i.e., V = 0). By perfectly aligning the Pitot tube with the flow, the flow will come to a stop at the tip of the Pitot tube, hence providing the stagnation pressure measurement.

Applying Bernoulli's equation between points 1 and 2 as shown in the figure, and canceling the elevations (equal values) gives,

Since V₂ = 0, the velocity at point 1 is

where p₁ and p₂ are known from the height of the fluid column in the piezometer and Pitot tube, respectively.

Energy and Hydraulic Grade Lines

fig. 3 Energy and Hydraulic Grade Lines

The energy grade line (EGL) and the hydraulic grade line (HGL) provide a graphical interpretation of Bernoulli's equation. The EGL represents the total head available with respect to a chosen datum (i.e., a reference line, as shown in the figure). The EGL is a constant for frictionless flow where no work or heat is associated with the process. On the other hand, the HGL is the sum of static pressure and elevation head.

Sometimes, this is also referred as the piezometric head and is the height a fluid column would rise in a piezometer. For example, the EGL and HGL for frictionless flow in a duct are shown in the figure.