This text is meant to accompany class discussions. It is not everything there is to know about fluids, hydrostatics, and fluid dynamics. It is meant as a prep for class.
All fluid flow is not alike. In the real world it is very complex and students earn doctorate degree just from doing intensive studies on fluid flow. Some fluids pour easily our of a glass, like water. Others flow more slowly, they even seem to pile up in the dish they land in. Viscosity describes the "thickness," or the level of internal friction. Water has a relatively low internal friction. Syrup, like maple syrup, has a high viscosity.
The blue fluid on left <– has a low viscosity. The orange fluid on the right -> has the higher viscosity.
Four rubber ducks are dropped in a river, and these floating rubber moved down the river side by side the whole way without bouncing up and down then the water is an example of laminar flow. The white lines in the diagram are called streamlines. For everything discussed here with moving fluids, the assumption is that all of the moving fluids exemplify laminar flow and streamlines are smooth and unbroken.
Viscosity keeps the fluid together like this. The viscosity can be broken down if the flow is too fast or if irregularities like obstacles are placed in the water.
Turbulent flow
The distance between the streamlines are no longer equal or when the streamlines break up, the flow is turbulent.
Flow Rate
The "flow rate" describes how quickly a volume of water flow by a point. It is a the conservation of mass is described for fluids moving through a pipe or stream. The variable for flow rate is not universal the way the variable for mass is. "Q" seems to be the most commonly used variable for the flow rate. So we will use "Q."
Below 3 pipes fill equal sized buckets. All of the pipes experience the same flow rate.
Think about the definition of "flow rate." How does this animation demonstrates equal flow rates?
The S.I. units of flow rate are .
Conservation of mass
Fluids must flow in such a way that they must conserve mass. If you have a pipe with different size opening, the amount of mass per unit time must be conserved to conserve mass in and out of the ends of the pipe.
Each blue cylinder in the animation above represent a volume of fluid. The volume on the left is equal to the volume on the right. Notice in the animation above that the left volume moves slower than the right side's volume. But each volume is defined by the same unit of time. (In the animation, the white circle for each shows the fluid flow through the same time interval.)
The Continuity Principle
Refer back to the pipe and fluids above.
For a single stream of constant fluid density, the continuity equation is,
This applies to laminar flow, not turbulent.
The "continuity principle" says that the flow rate must be maintained in a single stream to conserve mass. The animation below shows a boat drifting in the stream's flow.
Do you see how the two animations relate to each other?
The continuity equation says the flow rate is defined at any location, (location 1 or 2.) along the stream as the cross sectional area times the fluids velocity. It also says the flow rate is the same EVERYWHERE along a single stream flow. (Recall that that is conservation of mass.)
Below is a picture of a boat on a river. The river is flat because mass is conserved along the river. (This is an example of the law of conservation of mass.) The river speeds up and slows down to accommodate varying depths and widths along the stream. This makes the river flat.
If the continuity principle was not true, then mass could accumulate and the river could have bumps and dips along the surface for no apparent reason. The river might look like the one below. That's not a wave. Its a bump and a dip in the water's surface that just sits there. (Let's be clear. In reality, that does not happen.)
Can you guess where the flow rate is slowed down and where it sped up in the river above?
Example
Question
Solution
In order to pump a toy raft manufacturers have crafted a nozzle that fits over the end of a bicycle pump. It's dimensions are shown below. If air is pumped in to the large side on the left at 1.00 m/s, then how fast will it be traveling when it exits at the right?
Example
Question
Solution
For the piece of pipe show below, oil, (density = 700 kg/m3,) enters at opening 1 with a speed of 30 m/s. Opening 1 has a radius of 0.40 cm. The oil then exits at opening 2 where the radius is 0.15m. How fast is the oil traveling when it leaves the pipe at opening 2?
For the piece of pipe show below, oil, (density = 700 kg/m3,) enters at opening 1 with a speed of 30 m/s. Opening 1 has a radius of 0.40 cm. The oil then exits at opening 2 where the radius is 0.15 cm. How fast is the oil traveling when it leaves the pipe at opening 2?
A container of water has a hole poked into its side. The surface area of the top of the container is much larger than the hole. Water flows out of the hoie at constant rate. The water can fill up a smaller box with a volume of 5.40x10–5m every 2 seconds. The hole has a diameter of 0.01m. What is the velocity of the water as it pours out of the whole?
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
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