Next: , Previous: Previous Result, Up: Unit Expressions

### 5.6 Complicated Unit Expressions

The units program is especially helpful in ensuring accuracy and dimensional consistency when converting lengthy unit expressions. For example, one form of the Darcy–Weisbach fluid-flow equation is

      Delta P = (8/pi^2) rho f L (Q^2 / d^5)


where \Delta P is the pressure drop, \rho is the mass density, f is the (dimensionless) friction factor, L is the length of the pipe, Q is the volumetric flow rate, and d is the pipe diameter. It might be desired to have the equation in the form

        Delta P = A1 rho f L (Q^2 / d^5)


that accepted the user's normal units; for typical units used in the US, the required conversion could be something like

     You have: (8/pi^2)(lbm/ft^3)ft(ft^3/s)^2(1/in^5)
You want: psi
* 43.533969
/ 0.022970568


The parentheses allow individual terms in the expression to be entered naturally, as they might be read from the formula. Alternatively, the multiplication could be done with the ‘*’ rather than a space; then parentheses are needed only around ‘ft^3/s’ because of its exponent:

     You have: 8/pi^2 * lbm/ft^3 * ft * (ft^3/s)^2 /in^5
You want: psi
* 43.533969
/ 0.022970568


Without parentheses, and using spaces for multiplication, the previous conversion would need to be entered as

     You have: 8 lb ft ft^3 ft^3 / pi^2 ft^3 s^2 in^5
You want: psi
* 43.533969
/ 0.022970568