Water and other fluids move through pipes due to pressure gradients. In an ideal, level pipe without external pressure sources, the pressure will consistently decrease in one direction as the velocity increases, or vice versa. This is one way of stating the Bernoulli principle. The principle states that the total energy of a particle within a stream remains constant. You can use this principle to calculate the velocity of the fluid at a certain point downstream if you know the pressure drop and initial velocity. From this, you can calculate flow rate.
- Skill level:
- Moderately Challenging
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Things you need
- Venturi meter or pitot tube
- Measuring tape
Pick two points within the fluid stream to analyse. You will need to either know or have a way to measure the fluid velocity at point one. Therefore, it is often easiest to choose a stagnant locus for point one, such as in a reservoir connected to the pipe, if it exists.
Measure the pressure difference between point one and two. You can either do this with a venturi meter or pitot tube, which are both types of gauges for measuring fluid pressure.
Measure the height difference between point one and point two. Do not measure the actual length of pipe, but simply the downward distance, in the direction of gravity, that occurs between the two points.
Apply Bernoulli's equation. Bernoulli's equation states that the sum of energy due to pressure, altitude, and velocity at one point will be equal to the sum of energy due to these metrics at another point. Mathematically, it reads: P + 0.5 * rho * v^2 + rho * g * h = C. In this equation, P is pressure, rho is density of the fluid, g is acceleration due to gravity, and C is a constant. Substitute the appropriate values at point one into the Bernoulli's equation to obtain C. Then equate C to Bernoulli's equation at point two in order to solve for v.
Multiply v by the pipe's cross sectional area in order to obtain the flow rate. The cross sectional area of a pipe equals pi (or 3.14) times the square of its radius. You can determine the radius by measuring circumference and dividing by 2*pi.
Tips and warnings
- If you know the velocity at some point within the pipe that is near your point of interest, you can use that velocity directly in your flow rate calculation. Because water is mostly incompressible, velocity is conserved over lengths of pipe with uniform cross section.
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