If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Volume flow rate and equation of continuity

A fluid’s motion is affected by its speed, density, and viscosity, and weight, as wells as drag and lift. Use an example of a pipe with different sized openings on either end to observe and quantify laminar flow of liquids. Learn about the concept of flux, and how it is used to calculate the power of a system with moving fluid. Created by Sal Khan.

## Want to join the conversation?

• can you please tell me what does a venturi meter mean?
• A venturi meter is a way to measure flow in a pipe. The venturi is a section of pipe where the diameter is gradually reduced to some smaller area then gradually increased to the initial diameter

To measure the flow in the pipe you measure the pressure at the inlet and then again at the narrowest section of the venturi.

Assuming no friction. Conservation of energy tells you that the pressure in the reduced area will be lower because the velocity is increased (speeding a fluid up lowers it pressure, some what counter intuitive because we think of pressure in terms of force not potential energy)

Flow rate (Q) = velocity * Area

Q1 = Q2 v1 * A1 = v2 * A2

Potential Energy + Kinetic Energy remains constant. P1 + (1/2density *v1^2) = P2 + (1/density *v2^2)

you can solve these 2 equations for Q (refer to http://en.wikipedia.org/wiki/Venturi_effect)

• You appear to be saying that volume in = volume out only applies if laminar flow exists. Does this mean that fluid is lost or gained in the case of turbulent flow?
• Regardless of whether a flow is laminar or turbulent, if it is incompressible then volume in will always be equal to volume out. Since we're dealing with an incompressible liquid, this is always the case.

The example about emptying a bottle is a little confusing, because in that case the incompressible water is being replaced by air, which is very much compressible.
• Could you please tell me what kind of Flux Sal meant?because if he meant Momentum flux, the rate of transfer of momentum across a unit area, or Volumetric flux, the rate of volume flow across a unit area,why its far from his explaination about flux which he said its volume over time and its unit is m^3/s
• Hi there, I believe Sal has mixed up his terminology here.
He says that V/t is flux, but actually it is Volume Flow Rate, Q (units m^3/s).
Volumetric Flux is actually this flow rate per unit area, i.e. V/t.A, symbol q (units m^3/s.m^2).
• Is this the equation of continuity

• It is better known as 'Conservation of Mass'. Mass in = Mass out.
Since in the case Sal showed us there is mass flow (or mass flux), the flow into the nozzle must be equal to the flow out of the nozzle (because the flow can't go anywhere but out the other end). The flow at the entrance and the flow at the exit is given by the same equation (density)*(area)*(velocity).
• At , we should consider the time taken as dt 'coz the velocity changes as soon as the cross sectional area changes but for dt time we can assume that to be constant.
• He is simplifying the problem. He is considering the inlet velocity to be constant over the time of interest.
• Minute . I think it is actually in-viscid flow not laminar flow. As with laminar flow you can still have viscosity effects,...?
• Laminar flow is when a fluid flows in parallel layers with no disruption between the layers. Unless the wals of the container are frictionless the fluid next to the wall of the container that it is flowing through causes it to flow slower than the middle of the container causing a difference in velocity of the fluid. With low velocity and/or viscosity you can have laminar flow, above a critical velocity which is inversely dependent on the viscosity the flow will become turbulent. This ratio of a fluids velocity vs viscosity is related to the Reynolds Number for the fluid.
• how do we know that water is leaving from the entire output area of the cylinder as shown in the diagram? there aren't any forces pushing the water up so shouldn't the depth of the water in respect to the bottom of the cylinder remain constant throughout the cylinder?
• I think we are meant to imagine we are looking down at the pipe bird's eye view rather than from the side.
• The pipe is tilting downward but according to the equation Ai*Vi=Ao*Vo shouldn't the liquid decelerate instead. How is that possible?
(1 vote)
• He is not considering gravity. You interpret this problem as happening in a space station. Or that the pipe section shown is not vertical, but horizontal, so we see the pipe from above.