Resnick Halliday Krane Venturimeter formula mistake?

[KnightTheConqueror]

If this formula were to be correct, if we use the liquids in the Venturimeter and the tube to be of the same density, the velocity would come out to be zero which makes no sense. I calculated the formula and got a slightly different numerator. Am I correct?

 

[Filip Larsen]

My guess would be that it means that if the two fluids has same density then for any speed the interface between them will never "settle" at a fixed height difference but simply make a "flow loop". Or in other words, the formula as it is given has an implied condition that $\rho' > \rho$.