Consider a modified Bernoulli equation.
P + A ───── Bt² + ρg(h + Bt) + ½ρV² = constant
If t has the dimension of time then the dimensions of A and B ar $e _____,$ _____respectively.

Question

Consider a modified Bernoulli equation. P + A ───── Bt² + ρg(h + Bt) + ½ρV² = constant If t has the dimension of time then the dimensions of A and B ar e _____, _____respectively.

G1 Physics · Accepted Answer

Every term in the modified Bernoulli equation must have the dimensions of pressure. From the term h + Bt, we must have [Bt] = [h] = L. Since [t] = T, [B] = LT⁻¹. Now compare P with A ───── Bt² . Thus, [P] = [A] ──────── [B][t²] . Therefore, [A] = [P][B][t²]. Using [P] = ML⁻¹T⁻², [B] = LT⁻¹, [t²] = T², we get [A] = ML⁻¹T⁻² × LT⁻¹ × T² = MT⁻¹ = ML⁰T⁻¹. Hence, [A] = ML⁰T⁻¹, [B] = M⁰LT⁻¹. Correct option: B.