If V is a velocity, l a length, and v a fluid property having dimensions of L2T-1, which of the following combinations are qualitatively dimensionless (show work for a through d) : (a) V l v (b) Vl/v (c) V2v (d) V / (l v)

(b) Vl/v

Explanation:

The dimension for V is LT-1

The dimension for Length is L

The dimension for time is T

The fluid property v has a dimension of L2T-1, which is equal to square of the length divided by time.

for (a) Vlv

LT-1*L * L2T-1

= L^4T^-2

(b) Vl/v

LT^-1 * L / L^2 T^-1

=1.; this is dimensionless.

(c) V2v

(LT^-1) ^2 * L^2 T^-1

= L^4 T^-3

(d) V / (lv)

LT^-1 / (LL^2 T^-1)

= L^-2