Daniel Bernoulli was a Dutch-born Swiss mathematician whose 1738 study of hydrodynamics explored the basic properties in fluid flow. He lends his name to the formula that describes the inversely proportional relationship between flow rate and pressure. Bernoulli discovered that relationship by determining that the sum of the static, dynamic and gravitational pressures of a liquid remain constant. Manipulating Bernoulli's equation reveals either the flow rate or pressure depending on the available measurements.
Measure the difference in height between the surface of the water and the opening through which the water flows. Record the height and convert the measurement to meters. Divide the height difference in inches by 39.37 inches per meter to find the difference in meters.
Find the fluid velocity using the Bernoulli equation. Assume static pressure and multiply the height difference between the top of the hole and the surface of the fluid by 9.8 meters per seconds squared to account for acceleration due to gravity. Find the square root of the product multiplied by two to calculate fluid velocity in cubic meters per second.
Measure the density of the fluid by weighing one litre of fluid. The weight of one litre of fluid is its density if weight per litre. Convert to cubic meters by multiplying by .001 cubic meters per litre. Water has a standard density of 1000 kilograms per cubic meter at 4 degrees Celsius.
Calculate the Bernoulli constant by using the Bernoulli equation at a known pressure and velocity. Find the sum of the pressure plus the product of half the fluid density times the fluid velocity squared plus the product of the fluid density times 9.80 meters per second squared (the gravitational acceleration) times the height difference.
Find the flow pressure at the desired water rate by calculating the sum of half the fluid density times the fluid velocity squared plus the product of the fluid density times the gravitational acceleration times the height difference. Subtract that sum from the Bernoulli constant to determine the flow pressure at a given flow rate.