CHAPTER 2  BASIC CONCEPTS RELATED TO FLOWING WATER AND MEASUREMENT
3. Basic Principles of Water Measurement
Most devices measure flow indirectly. Flow measuring devices are commonly classified into those that sense or measure velocity and those that measure pressure or head. The head or velocity is measured, and then charts, tables, or equations are used to obtain the discharge.
Some water measuring devices that use measurement of head, h, or pressure, p, to determine discharge, Q, are:
(1) Weirs
(2) Flumes
(3) Orifices
(4) Venturi meters
(5) Runup measurement on a flat "weir stick"
Head, h, or depth commonly is used for the open channel devices such as flumes and weirs. Either pressure, p, or head, h, is used with tubetype flowmeters such as a venturi.
Pressure, p, is the force per unit area as shown on figure 21 that acts in every direction normal to containing or submerged object boundaries. If an open vertical tube is inserted through and flush with the wall of a pipe under pressure, water will rise to a height, h, until the weight, W, of water in the tube balances the pressure force, F_{p}, on the wall opening area, a, at the wall connection. These tubes are called piezometers. The volume of water in the piezometer tube is designated ha. The volume times the unit weight of water, ha, is the weight, W. The pressure force, F_{p}, on the tap connection area is designated pa. The weight and pressure force are equal, and dividing both by the area, a, gives the unit pressure on the wall of the pipe in terms of head, h, written as:
(21)
or:
(22)
Thus, head is pressure, p, divided by unit weight of water, , or 62.4 pounds per cubic foot (lb/ft^{3}). Pressure is often expressed in psi or pounds per square inch (lb/in^{2}), which may be converted to feet of water by multiplying the (lb/in^{2}) value by 2.31. For example, 30 lb/in^{2} is produced by 69.3 feet of water.

When the head principle is used, the discharge, Q, is computed from an equation such as the one used for a sharpcrested rectangular weir of length, L:
(23)
A coefficient, C, is included that accounts for simplifying assumptions and other deficiencies in deriving the equation. The coefficient can vary widely in nonstandard installations, but is well defined for standard installations or is constant over a specified range of discharge.
The flow crosssectional area, A, does not appear directly in the equation, but an area can be extracted by rewriting this equation:
(24)
in which:
(25)
In this form, C also contains a hidden square root of 2g, which, when multiplied by (h)^{1/2}, is the theoretical velocity. This velocity does not need to be directly measured or sensed. Because the weir equation computes velocity from a measuring head, a weir is classified as a head measuring device.
Some devices that actually sample or sense velocities, v, are:
(1) Float and stopwatch
(2) Current and propeller meters
(3) Vane deflection meters
These devices generally do not measure the average velocity, V, for an entire flow cross section. Thus, the relationship between sampled velocities, v, and the mean velocity, V, must be known as well as the flow section area, A, to which the mean velocity applies. Then, the discharge, Q, sometimes called the flow rate, is the product, AV.
Discharge or rate of flow has units of volume divided by unit time. Thus, discharge can be accurately determined by measuring the time, t, to fill a known volume, V_{o}:
(26)
Water measurement devices can be calibrated using very accurate volumetric tanks and clocks. More commonly, weight of water in the tanks is used by converting the weight of water per unit volume. The weight of water per cubic foot, called unit weight or specific weight, , is 62.4 lb/ft^{3} at standard atmospheric conditions.