Paper 2 · Moments and Equilibrium
The pressure p at a point in a fluid of density ρ moving with speed v is given as p = (1/2)ρv. Checking this using base units, which statement is correct?
A[ρv] works out to kg m^-1 s^-2, exactly matching the units of pressure, so the equation is dimensionally correct as printed.
B[ρv] works out to kg m^-2 s^-1, which does not match the units of pressure (kg m^-1 s^-2), so the equation is not dimensionally correct as printed.
CPressure has no fixed base units of its own, so no dimensional check can be applied to this equation.
D[ρv] works out to kg m^-3 s^-1, which happens to coincidentally match the base units used for density alone rather than pressure, so the equation is still treated here as dimensionally correct.
Explanation: [ρv] = (kg m^-3)(m s^-1) = kg m^-2 s^-1, but pressure has units kg m^-1 s^-2. These do not match, so the equation as printed is not dimensionally correct (the correct relation is p = (1/2)ρv², missing a factor of v).
Derived from ZIMSEC Physics Paper 2, November 2002, Q1