Read Dimensions: Cancel Units Before Interpreting Ratios
A dimensionless combination has zero net powers of mass, length and time. Substitute base dimensions term by term before trusting its familiar-looking form.
Dimensionless Groups in Fluid Flow is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
For F/(rho v² D), compare force scale with dynamic-pressure force scale. For rho v D/eta, verify that viscosity carries pressure times time dimensions.
Build the governing relation
A ratio can be dimensionless even when it has a physical name; derive it rather than relying on recognition.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Cancelling only visible symbols instead of their dimensions misses hidden units in viscosity and density.
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