How to derive velocity pressure in English units?

Question

I know that velocity pressure can be calculated from dynamic pressure according to the potential energy of pressure (from Bernoulli's equation):

$$ P = \frac{1}{2} \rho \overline{V}^2 $$

where P = dynamic pressure in Pascals, rho = density in kg/m^3, and V = velocity in m/s.

Solving for velocity gives:

$$ \overline{V} = \sqrt[]{\frac{2P}{\rho}} $$

I also believe that an equivalent formula (from this source) is:

$$ \overline{V} = 1096.7 \sqrt[]{\frac{P}{\rho}} $$

where P = dynamic pressure in inches of water, rho = density in kb/ft^3, and V = velocity in ft/min.

How is the last equation derived from Bernoulli's equation? I have been unable to verify the constant 1096.7.

Answer 1

It is converting units:

\begin{align} 196.9\,\bar{V}\,[m/s]&\longrightarrow \bar{V}\,[ft/min]\\ 0.0040\, P \,[pa] &\longrightarrow P \,[in\,w]\\ 0.0624\,\rho \, [kg/m^3] &\longrightarrow \rho\,[lb/ft^3] \end{align} So your factor is just $$ 196.9\sqrt{2\times\frac{0.0624}{0.0040 }} $$