# Stagnation tube

Flow through a sluice gate can be reasonably modeled using the Bernoulli equation.

The potential energy of the water behind the sluice gate is converted into kinetic energy as the water passes under the gate. Thus the velocity of the water can be calculated directly from the height of the water behind the sluice gate. Hydraulic jumps occur in open channel flow when the flow transitions from supercritical to sub critical flow (Munson, et al., 2002). The velocity in the channel can be determined by applying the Bernoulli equation in the region where velocity is increasing between the reservoir and immediately downstream of the sluice gate. The velocity can also be measured with a stagnation tube connected to a pressure sensor.

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The stagnation tube is filled with water prior to connecting to the pressure sensor and the pressure sensor output is zeroed with the stagnation tube held vertically (in the same orientation used for taking measurements.) Thus the pressure sensor will measure the pressure at point 3. From the Bernoulli equation across streamlines we can obtain the following relationship. Pitot tube is always placed directly upstream into the flow and is used to measure the difference between the pressure sensed by the Pitot tube and the pressure of the surrounding air flow. It always gives a very accurate measure of the velocity. In fact, it is probably the most accurate method available for measuring flow velocity on a routine basis and accuracies better than 1% are easily possible.

Bernoulli’s equation along the streamline that begins far upstream of the tube and comes to rest in the mouth of the Pitot tube shows the Pitot tube measures the stagnation pressure in the flow. Therefore, to find the velocity V, we need to know the density of air as opposed to in the stagnation tube, and the pressure difference. The density can be found from standard tables if the temperature and the pressure are known. The pressure difference is usually found indirectly by using a “static pressure tapping” located on the wall of the wind tunnel or on the surface of the model (Kermode, 1996).