Laminar Flow¶
Jack Hanlon, Forest Stothart
Spring 2021
The objective of this Laboratory Demonstration was to visualize Laminar Flow to our classmates, and to explain the effects of Reynolds number on the flow. It was conducted via three experiments: Osborne-Reynolds Apparatus, the Couette Cell and a punctured water-filled Balloon experiment.
Osborne-Reynolds Apparatus¶
In this experiment a tank filled with marbles (to help create laminar flow) and water has a central pipe that leaks a steady flow rate based on a valve opening. Dye is then injected into this flow to help visualize the flow type. The flow rate is then varied between Laminar flow, Laminar-Turbulent transitional flow, and then fully Turbulent flow. Reynolds number is then calculated from the measurements taken of flow rate, to show the Reynolds number ranges of the flow in a pipe with STP water. The Laminar flow was shown to have a single dye streak through the pipe. The Laminar-Turbulent transitional flow was Laminar at the beginning of the pipe and became turbulent further down the pipe, with the dye moving erratically in the fluid. Lastly, the Turbulent flow dye was erratic as soon as the dye entered the pipe.
Equipment¶
- Hydraulics Bench
- Osborne Reynolds Apparatus
- Ink/Dye (Orange/Black)
- Bucket
Cell phone stopwatch
Procedure:¶
Firstly, the Osborne-Reynolds Apparatus is placed on a table and filled with sufficient water using a pneumatic pump. The inflow control valve is left open to allow minimal overflow control of the tank. The pump was ran until the air bubbles were removed. Next the dye is added to the top inflow pipette and the outflow valve is opened to start a flow from the tank through the pipe and into the bucket. Dye is then slowly released into the system,flowing through the pipe, allowing for better visualization of the type of flow. The outflow valve is then opened and closed to measure Laminar and Turbulent flow. This was done by using a beaker and a stopwatch to measure the water that is flowing through the pipe/sec as an average of multiple attempts for each flow type.
Discussion:¶
The flow rate was tuned to produce Laminar flow, as shown in the first image, an orange dye streak outlines how the flow travels in a straight line. Orange dye happened to be difficult to view because over time it became thinner in the stream, so the dye colour was switched to black which became much clearer for the rest of the experiment. It was noted that Laminar flow was a very unstable flow as any perturbations to the table the apparatus was on would immediately turn the flow to turbulent (This occurred from actions such as leaning on the table or writing down calculations ). After looking at Laminar flow, the flow rate was increased until the flow was transitional and back to show the process of Laminar flow becoming Turbulent. It was noted that the turbulence appears first further down the stream in the pipe and then works its way up back until the entire pipe is turbulent. Therefore, there is a flow rate in which some of the flow is Laminar as it passes out of the tank and becomes turbulent as it travels through the pipe. Lastly, the turbulent flow was observed past a Reynolds number of 4000 and it was turbulent at a fully open outflow valve.
Hints:¶
- Make sure to check the outflow bucket often as it is of finite size, the lab floor eventually pays the price.
- When calculating turbulent flow rate it is better to leave the pump on, otherwise the tank drains too quickly and it is hard to take a measurement.
- The dye injection pipette can get air bubbles trapped in it that prevent the flow. To counteract this lift the pipette out of the tank and shake it to allow the air bubbles to escape, this should start the dye flow. (Be careful to keep the end over the hole into the tank otherwise ink will get spilled on the apparatus).
Results:¶
The Reynolds number was calculated for several different flow rates to characterize them. Using the equation:
$$Re = \frac{UD}{v}$$Where U is the 1D flow rate through the cross sectional area of the tube, D is the characteristic length scale, which in this case is the diameter of the cube, and $ν$ is the kinematic viscosity of water. In the experiment we measured the flow rate ‘u’ in $m^{3} s^{-1}$ , in order to convert this to the 1D flow rate, we divide by the cross sectional area of the tube.
$$A = \frac{1}{4}D^{2}$$To get $$Re = \frac{4u}{\pi D \nu}$$
Sample calculation using $u = 1.13\times 10^{-5} \frac{m^{3}}{s}$, $D = 1.2 cm$, and the kinematic viscosity for water at $20 ^\circ C$ : $$Re = \frac{4u}{\pi D \nu}$$
$$Re = \frac{4 ( 1.13\times 10^{-5})}{\pi (0.012m)(1.004\times 10^{-6} \frac{m^{2}}{s})}$$$$\therefore Re =1194.19$$
