Example: Consider a pitot tube suddenly immersed in a flow for velocity measurements. At the mouth of the tube the pressure will increase to , the total pressure. The pitot tube response is governed by the time taken by the entire tube to attain a uniform pressure . If the fluid as taken as incompressible then the pressure within the tube will adjust to instantaneously. Hence transients are related to the compressibility of the fluid. If is small, the fluid will behave as if it is nearly incompressible . However, the flexible tubing connecting the pitot tube to the manometer can be very long and of small diameter and hence have a large resistance. This can result in a finite time constant for the pitot tube and the associated tubing.

Let be the instantaneous pressure in the tube and be the resistance to the flow. Then the instantaneous flow is . Assuming laminar Poisseulle flow behaviour in the tube may be estimated as where is the tube length and the radius. This is the minimum resistance offered by the tube. Effects of flow development will increase the resistance beyond this value. Let be the volume of the tube . The additional flow will change the density of the fluid as