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Czech originalMeasurement of Air Velocity
In this contribution, I would like to convince you of two things. Firstly, physics is an experimental science, and as such it should be studied through participation in experiments at every opportunity. Simple experiments tend to be more enlightening, and it is useful to observe a particular physical phenomenon more than once, and even better to participate in a repetition oneself. I would suggest the creation of a store of simple and easily achievable experiments. They should be “plug and play” setups - single-purpose apparatus, waiting in a closet for you to need them. My second point is concerned with the importance of using different independent methods for measuring a physical quantity. Students should be convinced that the values of quantities are not just numbers, to which they arrived by more or less understood procedures. They should understand that there are other ways to achieve similar results.
Consider the following example, in which the volume of an aluminium cylinder is to be determined. In the sixth grade we can only use the direct method using a graduated cylinder. In the eighth grade, we can repeat the process and also calculate the volume from its dimension and using Archimedes’ principle. We may obtain the value of the desired quantity using three different methods, and all we need is an object of a proper shape, a graduate cylinder, a calliper and a spring scale. In addition, we can discuss the measurement accuracy of each method.
Measuring of the magnitude of air velocity is another example suitable for first-year students in high school. We need:
1. An air blower from the set for Molecular Physics, or from an air track. Even a smaller type of vacuum cleaner is sufficient, if need be.
2. A glass U-tube manometer, of about 30 cm long, filled with coloured water.
3. A flexible hose with aerodynamic nozzle, e.g. a roller ball tip. The wider end of the nozzle is inserted into the hose and we perform measurements with the narrow end.
4. A lightweight cart under the blower.
5. A spring scale of 2 N maximum range, and an approximately 60 cm long string with hooks for attaching the cart.
6. A right-angled triangle for measuring the height difference between the levels in the two arms of the manometer.
7. A retort stand with clamp for the manometer tube and a retort stand for the spring scale (we used 1 kg weight, spring scale was attached to it by the rubber band).
The setup for the experiment is depicted in Figure 1. One arm of the manometer is open, the second arm is connected by the hose to the nozzle put in the flow of the air. The height difference between the levels in the two arms of the manometer represents the ram pressure. According to the Bernoulli equation, we can obtain Δp = 1/2 ρw v2 and thus \[ v = \sqrt{\frac{2\Delta h \rho_w g}{\rho_{air}}} \] where Δh is the difference in level in the manometer, ρw is the density of the water, g is the acceleration of gravity and ρair is the density of the air which is dependent on temperature and pressure. You can find its value at specific conditions in tables of physical constants (the usually stated values are between 10-3kg·m-3 and 1.3·10-3kg·m-3). Independently of this method, it is possible to determine the air velocity by means of the reaction pulling force causing the accelerated motion of the blower. We determine the force using a spring scale or with the help of knowledge of the mass of the blower, distance and the time interval of the motion. From the equality between the change of the momentum of the air and the impulse acting upon it m·Δv = F·Δt we derive the formula with the help of students \[ v = \sqrt{\frac{F}{\rho_{\pi r^2 \rho_air}}} \] where F is the reaction pulling motion and r is the diameter of the discharge nozzle of the blower.
At the maximum power of the blower with a 32 mm diameter outlet we measured 12 cm difference between the levels, hence the magnitude of the air velocity is 47 m·s-1 in the centre of the jet. Thus the average air velocity across the whole cross sectional area of the jet is equal to 41 m·s-1 for the pulling force of 1.5 N.
I recommend the subsequent experiments:
• Measure the ram pressure and subsequently the magnitude of the air velocity in different parts of the cross sectional area of the blower outlet.
• Verify the independence of the ram pressure on the size of the cross sectional area of the nozzle (turn the wide end of the nozzle to the airstream).
• Expose the nozzle perpendicularly to the airstream and determine the underpressure in the nozzle (the principle of the airbrush). Verify again the independence of the underpressure on the size of the cross sectional area of the nozzle.
• Put a hose on the blower outlet and place a small light ball in the inclined airstream. With sufficiently laminar flow and a ball of small enough mass and adequately large diameter, it is possible to reach an inclination of the hose of under 45°.
• With the spring scale attached to the cart we cover the output of the airflow with our hand or, better still, with a smooth plate (textbook). Contrary to students’ expectations, the pulling force will sharply decrease. Using appropriate speed of airflow blowing against the barrier, the blower would even get attached to the plate.
Figure 1
Experiments suitable for a diversification of the teaching and a discussion of the physical phenomena
Flywheel
Get a flywheel from a discarded reel-to-reel tape recorder. It is perfectly balanced, mounted on a sufficiently long shaft with diameter measuring 4 mm to 6 mm. On one end, the shaft extends only a few millimetres and there is a pulley for a belt. On the other end, a few centimetres long, position two bearings on the shaft. Insert such mounted shaft into a tube of suitable diameter which is put loosely in a rubber band on the string. Wind a thin cord a few times around the pulley and spin it. The suspended flywheel maintains its horizontal axis and executes slow precessional motion. By changing the torsion of the suspension we can accelerate the motion, the shaft tilts upward, if we decelerate the motion, the shaft tilts downward.
Reverse Cartesian Diver
We prepare a Cartesian diver in a plastic bottle. I use a small test tube, coiled with a thick copper wire in such a manner that when completely filled with the air, only a few millimetres of the test tube are showing above the surface. Then we add extra weight for the diver to submerge. The bottle is opened and the test tube is at the bottom. Discussion follows about how to make the test tube ascend to the surface. Then squeeze the bottle gently and screw the cap on. After releasing the bottle, there is a lower pressure, the volume of the air in the test tube gets larger and the test tube ascends to the surface. The bottle is closed and the test tube is at the top.
Levitating Iron
Acquire a flat round ferrite magnet with a hole in the middle. The most suitable type is the one used in subwoofers. The magnets used in magnetrons from microwave ovens are also usable. Fill the centre hole with a cork. Stick a copper wire in the cork. Loosely put a soft iron tube on the wire. Determine the length of the tube experimentally. Ca. 3 cm is sufficient in my experience. The bottom of the tube is levitating between a few millimetres and one centimetre above the magnet level. See Figure 2.
Figure 2
Reaction motion, adiabatic process
We equip a plastic bottle screw cap with a valve stem of an older type of inner tube, in which a valve is only inserted and tightened with a lock nut. During compression the bottle gets warmer – adiabatic compression. After that we take the bottle around the cap with one hand and press the valve onto the table desk, using other hand we unscrew the lock nut. Then we release the cap. Compressed air blows out the valve and reaction force sends the bottle few metres high into the air. When it hits the ground, the bottle is cool – adiabatic cooling.
A few ideas at the end
• Do you need a truck, which can carry a lot, has low friction and costs nothing? Take two pairs of ball bearings from some discarded equipment (electric motors, printers, recorders, etc.). The pairs do not need to be identical. Put them on the shaft. A strong wire or a cut-off nail would suffice. Fix it in any way, axiality does not matter. Fasten shafts to a board using a rubber band and it is done.
• Do you need a metal tube? You can use a discarded freezer. From the freezer you acquire ca. 2 m iron tube and ca. one metre copper tube. Besides, the door is equipped with magnetic gasket along its entire perimeter, ideal for pinning up papers on a magnetic board. With a little skill, one can also utilise a compressor.
• Do you need strong magnets? Ask around about discarded speakers from radios and televisions, headphones, destroyed hard disk drives of the computers, magnetrons from microwave ovens, etc.