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LaTeX Math Inline
body\Delta p = p_1 - p_2

difference between pressure sensors readings

LaTeX Math Inline
body\Delta l

distance between pressure sensors

In case of stationary homogenous isothermal fluid flow the pressure gradient model can be correlated to fluid velocity as: 

LaTeX Math Block
anchor9KG06
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 G_p = G_{p0} + b \, q^n

The constant term 

LaTeX Math Inline
bodyG_{p0}
 is related to pressure gradient in static fluid column:

LaTeX Math Block
anchor1
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G_{p0} = \rho \, g \, \cos \theta

where

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LaTeX Math Inline
body\rho(T, p)

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Fluid density at a given location with pressure

LaTeX Math Inline
bodyp
and temperature
LaTeX Math Inline
bodyT

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LaTeX Math Inline
bodyg

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LaTeX Math Inline
body\theta

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See also

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Gradiomanometer @model

This make 

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G_p = a + b_l \, q^{n_l}+ b_t \, q^{n_t}

In smaller range of flowrate variations this can be simplified to: