# 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

## 3 Answers

You have to ask yourself -- what is driving the flow? Would the driver change or stay the same as your fluid changed? What are the variables conserved in a flow (ie. speed, energy, density, momentum, temperature, etc. -- I intentionally listed some that are conserved, some that are not).

In other words, think about how you are defining the problem. And how does the problem relate to the underlying laws of physics? If the mechanism driving the flow is the same in both cases, you will get a different answer than if the mechanism driving the flow changes.

Once you figure out what makes a fluid move, and then decide if that thing has changed or not, you can then decide what quantities are conserved. Once you figure those things out, in that order, you can decide how the speed changes as the density changes.

You could look at viscosity and its effects for yes, and at some never happened story of a guy dropping something from a tower and concluding something for no.

We're not allowed to give straight answers, so I hope this is vague enough.

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).