Pressure and velocity measurement devices

Measurement of static pressure

• Wall tap / piezometer: a small hole drilled flush with and normal to the wall, connected to a manometer or gauge. It reads static pressure because the streamlines at the wall run parallel to the wall, so a small flush hole does not disturb the flow. The hole must be small and burr-free.
• Piezometer tube: a vertical open tube connected to the wall tap; the liquid height gives the gauge pressure head. It is suitable only for moderate positive pressures in liquids.
• Static probe: a slender probe aligned with the flow, with small holes on its side, used inside the stream.
• Manometers and Bourdon gauges: read the pressure transmitted from the tap.

Pitot tube

A Pitot tube is a tube bent at right angles, with its open end facing the flow. The fluid at the tip is brought to rest (stagnation point), where its kinetic energy is converted into pressure.

Applying Bernoulli's equation between a point 1 upstream, where the velocity is $V$ and the pressure is $p$, and the stagnation point 0, where the velocity is zero:

$$\frac{p}{\rho g} + \frac{V^2}{2g} = \frac{p_0}{\rho g}$$

So the rise of liquid in the tube above the static level equals the velocity head:

$$h = \frac{V^2}{2g} \quad \Rightarrow \quad V = \sqrt{2gh}$$

In practice a coefficient $C_v$ (0.98 to 1.0) is included: $V = C_v\sqrt{2gh}$.

Pitot-static tube

It combines the Pitot tube (stagnation pressure) and a concentric outer tube with side holes (static pressure) in one probe, and connects both to a differential manometer.

                  stagnation hole
                        |
   ---------------------+-----> flow
   ===========[inner tube]=====> p0  to manometer
   ==[outer tube, side holes]==> p   to manometer
                   o  o  static holes

$$p_0 - p = \tfrac12\rho V^2 \quad \Rightarrow \quad V = C_v\sqrt{\frac{2(p_0 - p)}{\rho}}$$

For a differential manometer with reading $h_m$ of a fluid of density $\rho_m$, $p_0 - p = (\rho_m - \rho)g h_m$. Because the instrument gives the velocity at a point, the mean velocity in a pipe is found by traversing the cross-section.