25 Apr, 2013
In a bottles
PRESENTACIÓN: Vortices can be generated by joining two plastic bottles that are partially filled with liquid. The liquid falls in a spiral under the effect of gravity and an initial rotation. The same effect can be achieved with a single bottle with a hole made in the bottle top.
INTRODUCTION: This effect can essentially be explained by Bernoulli’s principle, assuming that the liquid used is incompressible and non-viscous.
OBJECTIVE: To observe the formation of a tornado.
MATERIALS: a plastic bottle, water, bottle top with a hole in it.
SETUP: For this experiment, a bottle is filled with water to 2/3 its capacity. A 1cm hole is perforated in the bottle top. Turn the bottle upside down and make the water go round in an anti-clockwise direction. A tornado will be formed inside the bottle.
EXPLANATION: Bernoulli’s principle is used for this experiment. The fluid must be incompressible, that is, it cannot change its volume and attempt to compress itself (its density is constant), and it must not be viscous, that is, there can be no friction between layers of fluid. We will assume that the only force acting on it is gravity, and that this is constant (cte). So, at each point in the fluid, Bernoulli’s principle is verified:
v2/2 + g z + p/ρ = cte
v is the velocity of the fluid at a point, ρ is the density, z is the height, g is the acceleration from gravity and p is the pressure. The constant is the same at every point in the fluid. We are going to assume that water is a non-viscous, incompressible fluid. Quickly stir it round. Once the stirring has stopped, we can assume that there are now no external forces affecting the fluid. Notice that a vortex is created with its central point lower than the rest of the points, and in which the linear velocity of the fluid is greater in the centre of the vortex and becomes less the further away from the centre it is. Let us consider an area of constant height z0 and use the principle. It tells us that half of the velocity squared plus the pressure over the density is a constant:
v2/2 + p/ρ = cte-g z0 = cte1
The velocity in the centre of the vortex is greater, which means that the pressure must be lower. As we move outwards, the speed reduces, which means that the pressure grows. Therefore, for a whirlpool like the one in the bottle to be produced, the pressure must increase as we move away from the vortex. Bernoulli’s principle also explains the curvature that the water in contact with the air has. The air has a pressure that is practically constant at the surface level, which we will call patm and this is approximately equal to 1 atmosphere. Then, the upper part of the water also has this pressure. Using Bernoulli’s principle for the surface of the water::
v2/2 + g z + = cte- patm/ρ = cte2
In the centre of the vortex, the speed is greater than at the edges, which means that the height (z) at the centre has to be lower than at the edges, which is precisely what is observed in the experiment.
CONCEPTS: atmospheric pressure, Bernoulli’s principle.
- R. Serway, Física, Mac Graw Hill, 2010.
- P. Tipler, Física para la Ciencia y la tecnología, Reverté, 2012.
- D.C. Giancoli, Física para Ciencias e Ingeniería, Pearson, 2009.
- D. Halliday, R. Resnick y J. Walker, Fundamentos de Física. CECSA, 2001.
STUDENTS 2011-2012: Marta González, Sandra Costoya
LINK pdf STUDENTS (in Spanish):