# Fluid speed and fluid density

How does fluid density affect fluid speed? Basically I am trying to figure out if, with all other quantities remaining constant, would an increase in fluid density cause the fluid speed to increase/decrease? For example, would water and honey have different fluid speeds in a pipe, because their densities are very different? I know that:

$$Av = Av$$

and

$$P + ρgh + (1⁄2) ρv^2$$

But does an increase in density lead to an increase/decrease in fluid speed? How so?

• You have to be more specific with respect to what other quantities do, when you increase the density. (That is, what specifically changes in what experimental/theoretical setup.) – Sebastian Riese Sep 13 '15 at 20:43
• I'm not an expert in fluid mechanics, but I think the speed would decrease. Isn't the viscosity of a fluid related to the density? I was reading about kinematic viscosity on Wikipedia. – zhutchens1 Jul 28 '16 at 22:16
• @zhutchens1 No, there is no general relationship between density and viscosity. Wtare and honey have very similar densities, but their viscosities are vastly different. – Pirx Jan 14 '17 at 17:23
• @trsfa I note that the expressions you wrote down make little to no sense. $A v=A v$ is trivial, and $p+\rho g h +\frac{1}{2}\rho v^2$ is just an expression that has dimension of volume-specific energy. Nothing follows from it. – Pirx Jan 14 '17 at 17:25

Continuity equation for $\textit{steady}$ flow, in which properties remain uniform over cross-section, is $\rho A v=$constant. If area remains constant along the flow then $v ~\alpha~ \frac{1}{\rho}$. For unsteady flow the statement is more complicated (read up compressible flows).