Convert 1 Pa s into poise using dimensional analysis

Step by step

1. The dimension of coefficient of viscosityCoefficient of viscosity has the dimensions [M L⁻¹ T⁻¹]. Only the powers of M, L and T matter for the conversion.
2. The conversion ruleA quantity with dimensions [M^a L^b T^c] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂] [L₁/L₂]⁻¹ [T₁/T₂]⁻¹.
3. The size of each base unitM: 1 kilogram (kg) is 1000 gram (g). L: 1 metre (m) is 100 centimetre (cm). T: 1 second (s) is the same in both systems.
4. Put the numbers inn₂ = 1 [1 kg / 1 g] [1 m / 1 cm]⁻¹ [1 s / 1 s]⁻¹
5. Work out each bracket[M₁/M₂] = 1000; [L₁/L₂]⁻¹ = 100⁻¹ = 0.01; [T₁/T₂]⁻¹ = 1⁻¹ = 1
6. Multiplyn₂ = 1 × 1000 × 0.01 × 1 = 10
7. The answer1 Pa s = 10 poise