Fluid Mechanics Calculator: Pressure, Buoyancy, Jets, Bernoulli, Viscosity and Stokes
Seven standard fluid mechanics calculations with every step shown: pressure at a depth, a manometer, buoyancy, a jet from a tank, Bernoulli, viscous shear and Stokes drag.
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Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
In a liquid at rest the pressure rises with depth, p equals rho g h. A U-tube manometer uses a second liquid to measure a pressure difference as a height difference. A body in a liquid feels an upward buoyant force equal to the weight of the liquid it displaces, so it floats if it is less dense than the liquid.
For flowing liquid, continuity says the flow Q equals area times speed everywhere along a pipe, and Bernoulli's equation trades pressure, speed and height along a streamline. The jet from a hole in a tank leaves at the speed a body would gain falling the same height. The Reynolds number says whether the flow is laminar or turbulent.
Viscosity is the resistance of a liquid to shear. Newton's law of viscosity gives the shear stress in a film as viscosity times the velocity gradient. For a small sphere sinking slowly, Stokes' law gives the drag force and the terminal speed.
Formulas used
- p = \rho g h
- \Delta p = (\rho_m - \rho) g h_m
- F_b = \rho g V
- v = \sqrt{2 g h}
- p_1 + \tfrac12\rho v_1^2 + \rho g z_1 = p_2 + \tfrac12\rho v_2^2 + \rho g z_2
- \tau = \mu \frac{U}{h}
- v_t = \frac{g d^2 (\rho_s - \rho)}{18\mu}
Worked example
With the default numbers in the calculator above:
- Gauge pressure at the depth: 29.37 kPa gauge
- The same in bar and in kPa absolute: 0.2937 bar gauge, 130.7 kPa absolute
- Force on a horizontal area of 1 m² at that depth: 29.37 kN
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
Does Bernoulli's equation include friction?
No. It is for ideal flow with no loss. It works well across a short contraction or a nozzle, and badly along a long pipe, where friction takes away head.
When does Stokes' law apply?
For a small sphere moving slowly, when the Reynolds number is below about 1. At higher speeds the drag is larger than Stokes' law predicts, and the calculator says so.
What density should I use for water?
About 998 kg/m3 at 20 degrees Celsius. Seawater is about 1025 kg/m3.
Why does the manometer result use the difference of densities?
Because the liquid in the pipe sits on top of the manometer liquid in both legs, so its weight is taken off the reading.
Related calculators
Further reading: White, Fluid Mechanics; Munson, Young and Okiishi, Fundamentals of Fluid Mechanics; Crane Technical Paper 410.
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