What you will learn
Use dimensional analysis; rearrange engineering equations; interpret linear and nonlinear graphs; calculate rates, efficiency and uncertainty; check whether a result is physically plausible.
Course syllabus
- 1. Quantities and units
Dimensional analysis: the fastest error detector
- 2. Equations and graphs
From formulas to trends, slopes and operating curves
- 3. Rates and evidence
Efficiency, change rates and measurement uncertainty
Free lesson · 32m
Dimensional analysis: the fastest error detector
Engineering calculations begin with quantities, units and dimensions. A number without a unit is rarely enough. Pressure may be expressed in Pa, kPa or bar; flow may be m³/h or L/s; energy and power are not interchangeable. Convert every input to a consistent system before substituting values.
Dimensional analysis tests the structure of an equation. Both sides must have compatible dimensions. For example, power = energy / time, so kWh divided by hours produces kW. If the units do not reduce to the quantity you expect, the calculation is not ready to trust.
Worked habit: write units beside every value, cancel them line by line and perform a rough order-of-magnitude estimate. A pump result of 500 MW for a small workshop system is a warning even if the calculator accepted every key press.
Keep units attached to values; convert before calculating; both sides of an equation need compatible dimensions; use order of magnitude as an independent check.