Fluid Mechanics @ UWA Transition to turbulence Aims Background Procedure Questions AIMS This experiment aims to investigate the transition from laminar flow in a tube to fully turbulent flow. You will use dye to qualitatively describe the transition point and also quantitatively determine the friction factor as a function of the flow Reynolds number. Background 1. Experimental Apparatus Specifications: Tube ID, d = 9.5 mm Test section length, L = 1 m Discharge cylinder ID, D = 90 mm r/ for the kerosene/water manometer = 0.2 2. Pipe flow The flow through a round pipe is characterised by the discharge velocity, V, the pipe diameter, D, the kinematic viscosity, , and the pipe wall roughness length scale, e. All properties of the flow are determined by this parameter set. For example the head loss due to friction, h , per unit length of pipe, L, is given by the following equation: (1) Dimensional analysis allows us to rewrite this equation as: (2) where, from Conservation of Energy, (3) ,(4) the Reynolds Number (ratio of inertia to viscous forces) and e D = relative roughness of the pipe. (5) One of the most intriguing features of pipe flow is that the form of the above function is dependent on whether the flow is laminar or turbulent. For small Reynolds number, the flow is laminar and viscosity is important in determining the head loss due to friction, while wall roughness is not important. As the Reynolds number increases viscosity plays a decreasing role and beyond a critical value, the flow becomes turbulent. On the other hand, the wall roughness becomes increasingly important since it is the roughness which determines the generation of the turbulence near the wall and therefore the shear stresses which determine head loss. Numerical analyses exist for the transition to turbulence in an infinitely long pipe. The results from these analyses show that the basic velocity profile of laminar flow is unstable at all Reynolds numbers. However the action of viscosity sets up a complicated retarding mechanism near the wall which is capable of damping out any tendency for the flow to become unstable (and thus turbulent) at Reynolds numbers below a critical value of about 10,000. However a laboratory investigation will differ from an infinitely long pipe in that it has an entrance and an exit. Whatever the exact configuration of these pipe ends, they may introduce disturbances which can trigger turbulence and so lead to a lower critical Reynolds number. As seen in Eq. 2 the head loss, h , is in general dependent on the Reynolds number and the relativeL roughness. Similarly Eq. 3 shows the parameterization for h based on the Conservation of Energy. If the L pipe in our experiment in horizontal (ie z =z ) and the flow is uniform (ie V =V ) then Eq. 3 becomes1 2 1 2 (6) You will need the Darcy-Weisbach Equation, derived in the Conservation of Energy laboratory notes (7) (Experimental results from Nikuradse) where f is the friction factor and is a function of Reynolds number and the relative roughness ratio, e/D. Theoretical and experimental expressions may be obtained for the friction factor by solving the momentum equation governing the flow in the tube. This yields the following results: Laminar flow (8) (from laminar flow theory) Turbulent flow - smooth wall (9) (Experimental results from Nikuradse) Turbulent flow - fully rough wall (10) (Experimental results from Nikuradse) Transition flow - rough wall (11) (Experimental results from Colebrook) Pre-lab question: Why is there a decrease in pressure between pressure sensors 1 and 2? Procedure 1. Identify the Discharge Control Valve; Discharge Cylinder; and the Manometer 2. Check that the leads from the two <a href="/keyword/pressure-transducer/" >pressure transducer</a> s are connected to the <a href="/keyword/pressure-transducer/" >pressure transducer</a> Interface on the wall. the <a href="/keyword/pressure-transducer/" >pressure transducer</a> Interface box is connected to the computer. the dye release mechanism ejects a satisfactory stream of dye. 3. Switch on the computer and the <a href="/keyword/pressure-transducer/" >pressure transducer</a> Interface (Conditioning Box). The data acquisition system used for this experiment records the change of pressure measured by one <a href="/keyword/pressure-transducer/" >pressure transducer</a> at the base of the Discharge Cylinder, which we will then use to calculate the flow rate in the pipe. the pressure difference measured at two points along the pipe and 1 metre apart, which we will use to calculate the friction factor 4. Start the data acquisition program by clicking the &quot;Transition to turbulence&quot; icon. The data acquisition program used in this laboratory has an interface that appears as below. The top left panel shows the height in curve. The bottom left panel shows the pressure difference between the two transducers in the pipe. While the middle column shows the water column in the Discharge Cylinder. Summaries of these plots are included in the bottom panels. Flow statistics are included in the lower right panel. 5. Set the sampling frequency to 20Hz. Note that a sample rate of 20 Hz means that a sample is taken every (1/20) seconds. 6. Set the flow rate by adjusting the Discharge Control Valve. 7. Close the valve at the bottom of the Discharge Cylinder but be careful not to let it overflow. 8. Release a thin stream of dye and record your observations in the table below. 9. Press the green button on the computer interface to begin sampling. Each sample should be 20 seconds. 10. Record H1 (the height of water in the Discharge Cylinder). 11. Press the red button on the computer interface to end sampling. 12. Record H2 (the height of water in the discharge cylinder). 13. Record the pressure difference from the Conditioning Box. 14. Record the pressure difference from the kerosene manometer. Be careful to let the kerosene manometer reach its equilibrium position, which can take a few minutes. 15. Note the location of the sample on the Moody diagram on the screen. 16. Check that your data is saved in the file...