Fluid Mechanics Calculator

Flow in a pipe becomes turbulent above a Reynolds number of roughly 4000 and is fully laminar below 2300. The transition zone between 2300 and 4000 can go either way. Water flowing at 1 m/s through a 25 mm pipe has a Reynolds number of about 25,000 - well into turbulent territory. The formula is Re = density times velocity times diameter divided by dynamic viscosity.

Multiply the cross-sectional area of the pipe by the flow velocity. A 50 mm diameter pipe carrying water at 2 m/s has an area of 0.00196 m squared, giving a flow rate of 0.00393 m cubed per second or about 3.93 liters per second. That is equivalent to roughly 62 gallons per minute.

Pascal's principle states that pressure applied to a confined fluid is transmitted equally in all directions. If a small piston (area 10 cm squared) pushes with 100 N, the pressure is 10 N/cm squared. A large piston with 200 cm squared area then exerts 2000 N - a mechanical advantage of 20. Real hydraulic car jacks use ratios of 10:1 to 50:1 to lift vehicles weighing several tons with hand-pump force.

Bernoulli's equation says that along a streamline, the sum of pressure energy, kinetic energy and potential energy per unit volume stays constant. When water speeds up through a constriction, its pressure drops - this is how a Venturi meter works. Narrowing a 50 mm pipe to 25 mm quadruples the velocity and drops the gauge pressure by roughly 24 kPa at typical household flow rates.

For turbulent flow, use the Darcy-Weisbach equation: delta-P = f times (L/D) times (density times V squared / 2). The friction factor f depends on Reynolds number and pipe roughness - for smooth commercial steel pipe at Re = 50,000, f is about 0.021. A 20-meter run of 25 mm pipe carrying water at 2 m/s loses roughly 67 kPa of pressure, equivalent to about 6.8 meters of head.