Investigating fluid dynamics and exploring the mathematics behind it.
This experiment demonstrates the dynamics of water owing out of a tank. Using the rate change of mass for an emptying cylinder, we investigate the application of Bernoulli’s equation and the resulting Torricelli’s theorem. We also observe the effects of construction on the parcel of water owing out of the tank. Students will investigate fluid dynamics, pressure and will relish how phenomena as simple as water coming out from a tank can lead to rich dynamics that can be explored mathematically.
- Fluid mechanics
- Bernoulli’s equation
- Torircelli’s theorem
- Equation of continuity
- Curve fitting and uncertainties
How Does it work?
The experiment comprises a graduated cylinder with an orifice positioned at a fixed height above the base. The cylinder is placed on PhysLoad, an electronic balance that reads the values of mass on the computer via a sophisticated homegrown data logging device and software, the PhysLogger.
As water flows out from the orifice, the PhysLogger records and plots the discharged mass of water in real-time. The collected data is used to determine the mass flow rate and linear speed v of water. Torricelli’s theorem derived from Bernoulli’s principle is applied to investigate the relationship between the height of the water and the linear speed of discharge. Further, a linear curve is fitted between v 2 and height h of water to observe the deviation of experimental data from theoretical results. Uncertainties are accounted for. The analysis of this experiment is displayed below.
- 1L graduated cylinder with an orifice
- Water guide
- Sink bucket
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