Bernoulli Mass Flow Rate Calculator

This calculation tool is designed to help you quickly and accurately determine the volume flow rate using the Bernoulli Equation. 
CalculationInputs﻿﻿d
:20m​
﻿
﻿﻿v
:21​
﻿
﻿﻿ρ
:2​
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Output﻿﻿Mass Flow Rate
:13194.6891​
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ExplanationIn fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy.
The Bernoulli equation states that
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P+12ρv2+ρgh=constantP +\frac{1}{2}ρv^2+ρgh = constantP+21​ρv2+ρgh=constant
Where:
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P=Pressureρ=flowdensityg=acceleration due to gravityv=velocityh=elevationP = Pressure \\ ρ = flow density \\ g = acceleration \: due \: to \: gravity \\ v = velocity \\ h = elevationP=Pressureρ=flowdensityg=accelerationduetogravityv=velocityh=elevation
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The principle is only applicable to isentropic flows. The equation is not valid when the flow is turbulent (the effect is irreversible) and for non-adiabatic processes (e.g. thermal radiation) because the effect is small.
💡 Who was Daniel Bernoulli?
The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book Hydrodynamica in 1738. Although, the Bernoulli equation stated that with an increase in flow speed, pressure decreases; it was Leonhard Euler in 1752 who determined Bernoulli's equation in its usual form. 
Calculating Mass Flow RateBernoulli equation can of course be rearranged to solve for each variable. Below presents a calculation to solve for m. 
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m=q . ρ=(π(d2)2v) . ρm = q\space .\spaceρ = (π(\frac{d}{2})^2v)\space.\spaceρm=q . ρ=(π(2d​)2v) . ρ
Where:
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m=mass flow rateq=volume flow rateρ=density fluidm = mass \: flow \: rate \\ q = volume \: flow \: rate \\ ρ = density \: fluidm=massflowrateq=volumeflowrateρ=densityfluid
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d=pipe diameterv=flow speedd = pipe \: diameter \\ v = flow \: speedd=pipediameterv=flowspeed
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