Consider a modified Bernoulli equation. ( P + A B t² )+ g(h+B t)+ 1 2 V²= constant If t has the dimension of time then the dimensions of A and B are _ _ _ _ , _ _ _ _ respectively.

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Correct answer: D. [ ML ⁰ ~T ⁻¹ ] and [ M ⁰ LT ⁻¹ ]

All terms must have dimension of pressure [ML⁻¹T⁻²] . For (h + Bt) : Since gh has dimension of pressure, [h] = [L] . For dimensional consistency: [Bt] = [L] , so [B] = [LT⁻¹] = [M^0LT⁻¹] For A Bt^2 : [A] [B][T^2] = [ML⁻¹T⁻²] [A] = [B][T^2][ML⁻¹T⁻²] = [LT⁻¹][T^2][ML⁻¹T⁻²] = [ML^0T⁻¹] [A] = [ML^0T⁻¹] and [B] = [M^0LT⁻¹]

Consider a modified Bernoulli equation. ( P + A B t² )+ g(h+B t)+ 1 2 V²= constant If t has the dimension of time then the dimensions of A and B are _ _ _ _ , _ _ _ _ respectively.

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