Worked Examples
Browse common examples from different branches of math, each written with clear step-by-step instructions.
Showing 4 worked examples in Engineering.
Calculate the moment of inertia of an I-beam
The strong-axis second moment of area of an I-beam, found two ways: subtract the empty pockets from the outer rectangle, or add the flanges and web with the parallel axis theorem. Both give for a 150 by 250 mm section.
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Calculate a compound gear ratio
A compound gear train multiplies the ratios of its stages. Two stages give , so rpm in becomes rpm out and the ideal torque is multiplied by .
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Calculate flow rate from pressure and pipe diameter
Pressure and diameter alone do not fix a flow rate. What the pressure is doing decides the method: a known velocity gives , an orifice turns a pressure difference into flow, and a long pipe loses pressure to friction and has to be solved by iteration.
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Calculate pressure drop from flow rate
With the flow known, pressure drop in a pipe is a direct calculation: find the velocity, the Reynolds number, the friction factor, then apply Darcy-Weisbach and add fitting losses. For L/s through m of mm pipe with two elbows it comes to about kPa.
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