<Dl> <Dd> δ ψ i n = δ ψ o u t (\ displaystyle \ delta \ psi _ (in) = \ delta \ psi _ (out) \,) </Dd> <Dd> u δ y + v δ x = (u + ∂ u ∂ x δ x) δ y + (v + ∂ v ∂ y δ y) δ x (\ displaystyle u \ delta y + v \ delta x \ = \ left (u+ (\ frac (\ partial u) (\ partial x)) \ delta x \ right) \ delta y+ \ left (v+ (\ frac (\ partial v) (\ partial y)) \ delta y \ right) \ delta x \,) </Dd> </Dl> <Dd> δ ψ i n = δ ψ o u t (\ displaystyle \ delta \ psi _ (in) = \ delta \ psi _ (out) \,) </Dd> <Dd> u δ y + v δ x = (u + ∂ u ∂ x δ x) δ y + (v + ∂ v ∂ y δ y) δ x (\ displaystyle u \ delta y + v \ delta x \ = \ left (u+ (\ frac (\ partial u) (\ partial x)) \ delta x \ right) \ delta y+ \ left (v+ (\ frac (\ partial v) (\ partial y)) \ delta y \ right) \ delta x \,) </Dd> <P> and simplifying to: </P>

Show that the flow rate between any two streamlines