Question

An equation for the frictional pressure loss Δ p (inches H2O) in a circular duct of inside diameter d (in.) and length L (ft) for air flowing with velocity V (ft/min) is Δp = 0.027( L d 1.22)(V V0)1.82,where V0 is a reference velocity equal to 1000 ft/min. Find the units of the "constant" 0.027.

Answer 1

Answer:

The units of the constant "0.027" is inchH₂O·inch^(1.22)/fit

Explanation:

The constant has to be consistent with all the other units of this equation:

$\Delta P [InH_2O]=\displaystyle 0.027[x]\frac{L[ft]}{(d[in])^{1.22}}(\frac{v[ft/min]}{v_0[ft/min]})^{1.82}$

Therefore:

$[InH_2O]=\displaystyle [x]\frac{[ft]}{([in])^{1.22}}(\frac{[ft/min]}{[ft/min]})^{1.82} \leftrightarrow [x]=\frac{[InH_2O][in]^{1.22}}{[ft]}$