Unity brackets PDF

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Unity brackets...

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Unity Brackets A unity bracket is a dimensionless [0] ratio of two identical quantities, for example: [1 Inch/0.0354m] [1hp/746W] [1000J/1kJ] [105Pa/1 bar] To convert 30 mile/gal into standard SI units, we need to change miles to km and gallons to litres, using the appropriate unity brackets. Multiply by unity brackets as many times as necessary to convert all units… = 30 mile/gal = (30 mile/gal) x (1.60934 km/1mile) x (1gal/4.54609 litre) =((30 x 1.60934)/(4.54609)) x ((mile x km x gal)/(gal x mile x litre)) = 10.61 km/litre

In a worded style question, the same process applies: A torque input to a centrifugal pump is measured using an old “Imperial” unit with a weight of 7.3 lbf, acting at a lever arm of 1 foot. Identify the SI value (in Nm) of this torque using the conversions: 1 m = 3.281 ft and 1 lbf = 4.45 N = = = =

7.3 ft x lbf (7.3 ft x lbf) x (1m/3.281 ft) x (4.45N/1 lbf) ((7.3 x 4.45)/(3.281)) x ((ft x lb x ft x m x N)/(ft x lb x ft)) 9.9 Nm

Note the difference between mass and weight; mass is just the amount of matter in an object, whereas weight accounts for gravitational forces too, and gives the force exerted on the object by gravity. Mass has units such as kg and lb, whereas weight is a force so has units like kp (kilopound), N and lbf. Remember that 1 Pa = 1 N/m2 and that 105 N/m2 = 1 bar....