# Bernoulli's Principle

Ask yourself the following question; does atmospheric pressure increase in a gale, tornado or hurricane?

Believe it or not, the answer is no. High-speed winds may blow the roof off your house, but the pressure within the winds is actually less than that of the still air of the same density inside the house. As strange as it may first seem, when the speed of a fluid increases, the internal pressure decreases proportionally. This is true whether the fluid is a gas or a liquid.

Daniel Bernoulli, a Swiss scientist of the 18th Century, studied the relationship of fluid speed and pressure. When a fluid flows through a narrow constriction, its speed increases. This is easily noticed by the increased speed of a stream when it flows through the narrow parts. The fluid must speed up in the constricted region if the flow is to be continuous. Bernoulli wondered how the fluid got the energy for this extra speed.

He reasoned that the energy is acquired at the expense of a lowered internal pressure. His discovery, now called Bernoulli's Principle, states:

The pressure in a fluid decreases as the speed of the fluid increases.

Bernoulli's Principle is a consequence of the conservation of energy. When a fluid flows, it has kinetic energy because of its motion. It also has gravitational potential energy, or stored energy due to the Earth's gravitational field. If the fluid picks up speed, or accelerates, it has more kinetic energy than before. Let's suppose that the fluid does not move up or down as it travels through the constricted region. Then its gravitational potential energy does not change. How, then, does the accelerating fluid in the constricted region gain kinetic energy?

The answer is that the surrounding fluid does work on the part that goes through the constricted region. The accelerating fluid is pushed from behind by the forces that produce pressure. They do work on the accelerating fluid and the accelerating fluid has to do work on the fluid ahead of it. It turns out that when the fluid is accelerating, more work is done on it than it does on the fluid ahead. In this way, its kinetic energy increases.

All through the fluid, some parts are gaining energy while others are losing energy. The net energy of the entire fluid is unchanged.

Bernoulli's Principle holds for steady flow. In steady flow, the paths taken by each little region of fluid do not change as time passes, and can be represented in a diagram with streamlines, which are the smooth paths of the neighbouring regions of fluid. The lines are closer together in the narrower regions, where the flow speed is greater and the pressure within the fluid is less.

If the flow speed is too great, the flow may become turbulent and follow changing, curling paths known as eddies. Then Bernoulli's Principle will not hold.

### Dangers

Bernoulli's Principle accounts for the fact that passing ships run the risk of a sideways collision. Water flowing between the ships travels faster than the water flowing past the outer sides, so the streamlines are more compressed. Water pressure is reduced between the ships. Unless the ships are steered to compensate for this, the greater pressure on the outer sides of the ships then forces them together.

At the start of this entry, it was stated that air pressure drops in a tornado or hurricane. As it turns out, a house with no vents and airtight closed doors is in more danger of losing its roof than a well-vented building. This is because the air pressure inside is higher than that outside. Therefore, it is more likely for the roof to be pushed off than blown off.

If the roof is peaked, the effect is even more pronounced. The difference in pressure need not be much, but over a large area a small pressure difference can be formidable. So, if you are ever caught in an unvented building in a hurricane, consider opening the windows so pressures are more or less equal1.

### Usefulness

Looking at a blown-off roof as a primitive aeroplane wing, it is easier to understand the lifting force that supports a heavy airliner. In both cases, a greater pressure below pushes the roof and wing into regions of lesser pressure above. An arched roof is more apt to be blown off than a flat roof. Similarly, a wing with more curvature on the top surface has greater lift than a wing with flat surfaces, such as the wings of children's balsa-wood gliders. Whether it has flat or curved wings, an airplane will fly by virtue of air impact against the lower surface of wings that are tilted back slightly to deflect oncoming air downwards. The airfoil of a curved wing, however, adds considerably to lift and results in a greater difference in pressure between the lower and upper wing surfaces. This net upward pressure multiplied by the surface area of the wing gives the net lifting force. The lift is greater when there is a large wing area and when the plane is travelling fast. Gliders have a very large wing area so that they do not have to be going very fast for sufficient lift. At the other extreme, fighter planes designed for high speed have very small wing areas. Consequently, they must take off and land at relatively high speeds.

A baseball pitcher can throw a ball in such a way that it will curve off to one side of its trajectory. This is accomplished by imparting a large spin to the ball. Similarly, a tennis player can hit a ball that will curve. A thin layer of air is dragged around the spinning ball by friction, which is enhanced by the baseball's threads or the tennis ball's fuzz. The moving layer produces a crowding of streamlines on one side.

The net force produced by unequal pressures is not restricted to spinning balls. Bernoulli's Principle has been applied with varying degrees of success to sailboats without sails since the 1920s. In the place of masts, these ships have large motor-driven vertical cylinders that rotate about their vertical axes. Like the case of the spinning baseball, a net force is produced that moves the ship, in most cases, more efficiently than canvas sails. A more recent design is Jacques Cousteau's ship, the Alcyone. Instead of rotating cylinders, it has fixed cylinders with special venting and equipped with an internal fan to produce the unequal pressures. Conventional diesel engines power the ship when wind speed is insufficient. With a good wind, Alcyone can save over 50% in fuel, and with winds over 25 knots (12.5 metres per second) the diesel engines can be shut off altogether for a cruising speed of 9 knots2.

Both prairie dog warrens and tenement buildings utilise Bernoulli's Principle for ventilation. The prairie dog warrens stretch for long distances underground, with openings at different altitudes. Because higher places are windier, atmospheric pressure is reduced, causing air to flow through their tunnels from outlets in higher pressure areas to outlets in lower pressure areas. The same principle applies in apartment buildings with air-shafts. Because the air-shaft is open only at the windy roof, fresh air is drawn through an apartment from the level windows through the air-shaft.

### Demonstrating Bernoulli's Principle

Hold a sheet of paper in front of your mouth. When you blow across the top surface, the paper rises. This is because the moving air pushes against the top of the paper with less pressure than the air that pushes against the lower surface, which is at rest.

Bernoulli's Principle can be simply demonstrated by taking a shower. Turn on the shower full blast and get in. Air near the water stream flows into the lower pressure stream and is swept downward. Air pressure inside the curtain is reduced and the curtain is pushed inward. So the next time a freezing cold shower curtain wraps round your legs, think of Daniel Bernoulli!

1A word of warning; opening the windows of a building with adequate venting may actually increase the risk of damage.2A knot is a nautical mile per hour, approximately 1.15 land miles per hour.