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Venturi Flow Rate

The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. The Venturi flow rate is the volume flow of the fluid as it passes through that choke as measured by a Venturi flow meter.

The flow rate increases linearly with the discharge coefficient and the square root of the difference between upstream and downstream pressures. As the upstream pipe diameter approaches the downstream pipe diameter, the flow increases. The flow rate decreases inversely with the square root of the fluid density.

Formula

QuantityVariable["Q", "VolumeFlow"] == (Pi*QuantityVariable["C", "Unitless"]*QuantityVariable[Subscript["D", "1"], "Diameter"]^2*Sqrt[(QuantityVariable[Subscript["P", "1"], "Pressure"] - QuantityVariable[Subscript["P", "2"], "Pressure"])/QuantityVariable["ρ", "MassDensity"]])/(2*Sqrt[2]*Sqrt[-1 + QuantityVariable[Subscript["D", "1"], "Diameter"]^4/QuantityVariable[Subscript["D", "2"], "Diameter"]^4])

symbol description physical quantity
Q flow rate "VolumeFlow"
C discharge coefficient "Unitless"
D1 upstream pipe diameter "Diameter"
D2 downstream pipe diameter "Diameter"
ρ fluid density "MassDensity"
P1 upstream pressure "Pressure"
P2 downstream pressure "Pressure"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Venturi Flow Rate"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Venturi Flow Rate"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Venturi Flow Rate"], {QuantityVariable[ \!\(\*SubscriptBox[\("P"\), \("2"\)]\),"Pressure"] -> Quantity[20, "Pascals"], QuantityVariable[ \!\(\*SubscriptBox[\("D"\), \("1"\)]\),"Diameter"] -> Quantity[0.02`, "Meters"], QuantityVariable["\[Rho]","MassDensity"] -> Quantity[1000, ("Kilograms")/("Meters")^3], QuantityVariable[ \!\(\*SubscriptBox[\("P"\), \("1"\)]\),"Pressure"] -> Quantity[40, "Pascals"], QuantityVariable["Q","VolumeFlow"] -> Quantity[100, ("Liters")/("Seconds")], QuantityVariable[ \!\(\*SubscriptBox[\("D"\), \("2"\)]\),"Diameter"] -> Quantity[0.01`, "Meters"]}]
Out[3]=

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