The Pitot tube
The Pitot tube is used to measure the difference between the impact and static pressures in a fluid. It normally consists of two concentric tubes arranged parallel to the direction of flow; the impact pressure is measured on the open end of the inner tube. The end of the outer concentric tube is sealed and a series of orifices on the curved surface gives an accurate indication of the static pressure. The position of these orifices must be carefully chosen because there are two disturbances that may cause an incorrect reading of the static pressure. These are due to:
(1) The head of the instrument
(2) The portion of the stem which is at right angles to the direction of flow of the fluid.
These two disturbances cause errors in opposite directions, and the static pressure should therefore be measured at the point where the effects are equal and opposite.
If the head and stem are situated at a distance of 14mm diameters from each other as on the standard instrument. The two disturbances are equal and opposite at section 6mm diameters from the head and 8mm from the stem. This is, therefore, the position at which the static pressure orifices should be located. If the distance between the head and the stem is too great, the instrument will be unwieldy; if it is too short, the magnitude of each of the disturbances will be relatively great, and a small error in the location of the static pressure orifices will appreciably affect the reading.
For Reynolds numbers of 500-300,000, based on the external diameter of the Pitot tube, an error of not more than 1 percent is obtained with this instrument. A Reynolds number of 500 with the standard 7.94 mm pitot tube corresponds to a water velocity of 0.070 m/s or an air velocity of 0.91 m/s. Sinusoidal fluctuations in the flow rate up to 20 percent do not affect the accuracy by more than 1 percent, and calibration of the instrument is not necessary.
A very small pressure difference is obtained for low rates of flow of gases, and the lower limit of velocity that can be measured is usually set by the minimum difference in pressure that can be measured. This limitation is serious, and various methods have been adopted for increasing the reading of the instrument although they involve the need for calibration. Correct alignment of the instrument with respect to the direction of flow is important; this is attained when the differential reading is maximum.
For the flow not to be appreciably disturbed the diameter of the instrument must not exceed about one-fiftieth of the diameter of the pipe; the standard instrument (diameter 7.94 mm) should therefore not be used in pipes of less than 0.4 m diameters. An accurate measurement of the impact pressure can be obtained using a tube of very small diameter with its open end at right angles to the direction of flow; hypodermic tubing is convenient for this purpose. The static pressure is measured using a single piezometer tube or a piezometer ring upstream at a distance equal approximately to the diameter of the pipe and measurement should be made at least 50 diameters from any bend or obstruction.
The Pitot tube measures the velocity of only a filament of fluid, and hence it can be used for exploring the velocity distribution across the pipe section.
Although a single pitot tube measures the velocity at only one point in a pipe or duct, instruments such as the averaging pitot tube or Annular, which employ multiple sampling points over the cross-section, provide information on the complete velocity profile which may then be integrated to give the volumetric flow rate. An instrument of this type has the advantage that it gives rise to a lower pressure drop than most other flow-measuring devices
Pitot tube working procedure and calculation to find the velocity of a stream:
To measure local velocity in a pipe or to calculate a point velocity in an open-air stream Pitot tube is used. It works on the principle of using pressure difference to find the velocity between the pressure points of measuring. It is simple in construction and easy in application, let’s make ourselves comfortable to understand how a pitot tube can help in determining a velocity variable. A manometer that is filled with a manometric fluid such as mercury or ccl4 can find the pressure difference when connected to the Pitot tube outlet endpoints. The Pi, impact pressure, and Po, static pressure are pressures obtained from the pitot tube. Impact pressure is the pressure that is exerted by the fluid when a tube is inserted in its flow stream and static pressure is the pressure exerted by the fluid on the side wall of the tube at the same position.
Velocity = C × √2g∆h = C× √2g(Pi-Po)ρ
Where:
C= coefficient
g=dimensional constant
ρ= density of the fluid
The coefficient C is about 1.00 (±0.01) for simple Pitot tubes and for Pitot-static tubes it may be around 0.98 to 1.00.
Problem:
Calculate the velocity of water flowing in a pipe installed with a pitot tube which has a coefficient of 0.98 and a stagnation pressure is 5.67 m and a static pressure head in the pipe is 4.73 m.
solution:
Between two points A, B where B is the stagnation point where zero velocity is developed which is at the open end of the tube, by applying Bernoulli theorem form A to B where A is the point at which the static point is taken
(PA + V A 2 / 2g + 0) – no loss = (PB + 0 + 0 )
VA = √2g(PB-PA)
= 0.98√2g(5.67-4.73)
= 4.21 m/s
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