Two Formulas for Combinations of Restrictors

Lohm Laws

**For parallel flow,** the total Lohm rating is:

\[\frac{1}{L_T}=\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{L_3}+…+\frac{1}{L_N}\]

Please note that this relationship is identical to the electrical equation.

**Example 1:** Parallel flow

L_{1} = 2000 Lohms

L_{2} = 3000 Lohms

L_{3} = 5000 Lohms

\[\frac{1}{L_T}=\frac{1}{2000}+\frac{1}{3000}+\frac{1}{5000}=0.00103\]

and therefore L_{T} = 970 Lohms

**For series flow,** the total Lohm rating is:

\[L_T=\sqrt{L_1^2+L_2^2+L_3^2+…+L_N^2\ }\]

Please note that this relationship is not the same as in electrical problems. The difference is due to the non-linearity of:

\[H=\frac{I^2L^2}{400}\]

**Example 2:** Series flow

\[L_T=\sqrt{2000^2+3000^2+5000^2}=6160\ \,\text{Lohms}\]

When L_{1} = L_{2} = L_{3}, then L_{T} = L √N

N = Number of equal resistors in series

For passageway size, D_{T} = D/N^{1/4}

D_{T} = Diameter of a single equivalent orifice, with a Lohm rate = L_{T}

D = Diameter of the actual orifices, each with a Lohm rate = L_{1}

One of the reasons for using two restrictors in series is to allow fine-tuning of a total resistance value. If L_{1} is known and is more than 90% of L_{T}, then L_{2} may vary by ±5% without altering the value of L_{T} by more than ±1%, even though the value of L_{2} may be as high as 40% of L_{T}. This effect becomes even more pronounced as L_{1} approaches L_{T}.

To determine the intermediate pressure between two restrictors in series, the following formulas may be used.

\[\Delta\ P_1=\frac{\Delta\ P_T\ }{1+\left(\frac{L_2}{L_1}\ \right)^2\ }\]

\[\Delta\ P_2=\frac{\Delta\ P_T\ }{1+\left(\frac{L_1}{L_2}\ \right)^2\ }\]

\[\left(\frac{L_1}{L_2}\ \right)^2=\frac{\Delta\ P_1\ }{\Delta\ P_2}\]

Always verify flow calculations by experiment.

^{*}There are many parameters to consider when determining V-Factor. **Click here** for more information.