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By the way, even if you're just doing a quick calculation, I recommend not using a calculator. Enter the data into an Excel spreadsheet so that you can add/change/scrutinize/save calculations as needed. Sometimes I see an obviously invalid result and when I ask, ""How did you get that resulti) What numbers did you usei)“ the answer is ""I put the numbers into the calculator and this was the result I got.“ But how do you know you entered the numbers and formulas correcdyi) What if you need to re‐do the calculation for a slightly different set of numbersi)

Examples of the use of units and scrutiny

These examples, particularly the first one, also introduce the concept of ""back of the envelope“ estimates, a powerful engineering tool.

Example 1. Drag force and power requirements for an automobile

A car with good aerodynamics has a drag coefficient (C) of 0.2. The drag coefficient is defined as the ratio of the drag force (F) to the dynaRejectppcpreJJ'ure of the flow =1/2pv2 (where p is the fluid density and v the fluid velocity far from the object) multiplied by the cross‐section area (A) of the object, i.e.

FD=12CDρv2A (Equation 7)

The density of air at standard conditions is 1.18 kg/m3.

(a) Estimate the power required to overcome the aerodynamic drag of such a car at 60 miles per hour.

Power = Force x velocity

v=60 miles/hour x (5280 ft/mile) x(m/3.28ft)x(hour/60min)x(min/60s)=26.8m/s

Estimate cross‐section area of car as 2 mx3m=6m2

FD=0.5x0.2x1.18kg/m3x(26.8m/s)2x6m2=510 kg m/s2=510 Newton

Power =FDxv=510 kg m/s2x26.8m/s=1.37x104 kg m2/s3=1.37x104W=18.3 horsepower, which is reasonable

(b) Estimate the gas mileage of such a car. The heating value of gasohne is 4.3 x107J/kg and its density is 750 kg/m3.

Fuel mass flow required = power (Joules/s)/ heating value (Joules/kg)

=1.37x104 kg m2/s3/4.3x107J/kg=3.19x10-4kg/s

Fuel volume flow required = mass flow / density

=3.19x10-4kg/s/750kg/m3=4.25x10-7m3/sx (3.281 ft/m)3x7.48 gal/ft3 =1.12x10-4 gal/sec