While land animals often have awkward, non-aerodynamic shapes, sea animals are usually pretty streamlined. That difference is explained by the enormously greater forces of water resistance as compared to air resistance. In a nutshell, a non-hydrodynamic sea animal had better have a thick shell, taste lousy, or expect to be eaten.

Dolphins are a case in point. They have evolved wonderfully streamlined and hydrodynamically efficient shapes. The interactions between a dolphin and the water around it offer many opportunities to examine the physics of fluids and motion.

1. While a dolphin is a mammal and all mammals have hair, what few whiskers the dolphin develops during gestation are lost around the time of birth. The result is that dolphins have as little surface area as possible for their basic size and shape. Why does minimizing its surface area tend to make the dolphin more energy efficient while swimming through the water? (Note: ignore issues related to golf ball dimples or tennis ball fuzz, which are not relevant to this question.)

Answer: Minimizing its surface area allows the dolphin to reduce the viscous drag it experiences as it moves through the water.

Why: The more wetted surface that the dolphin has, the more it rubs on the water as it passes and the more of that water it pulls along with it. By keeping its surface area to the lowest practical value, the dolphin minimizes the amount of surface friction-like forces it experiences from the passing water.

2. In addition to having a small surface area, the dolphin has a remarkably streamlined shape. Its nose and head curve out and back, with no sharp edges or forward-projecting appendages. The dolphins body reaches its maximum girth about a third of the way from its nose to tail and then the dolphin's body tapers gradually to a narrow tip that finally ends in its broad, flat tail fluke. Because of this carefully developed shape, the dolphin creates almost no turbulent wake when it moves through the water. Why does the near absence of a wake make the dolphin more energy efficient when it swims?

Answer: The smaller the dolphin's turbulent wake, the less pressure drag the dolphin experiences.

Why: Turbulent wake and pressure drag go hand-in-hand. By parting the water smoothly and keeping the flow attached to its body until that water passes its tail fluke, the dolphin ensures that the pressures that push on its front-facing surfaces are balances by pressures that push on its rear-facing surfaces. The result is a nearly balanced distribution of pressures between front and back and a virtual absence of pressure drag on the dolphin.

3. Imagine that you are riding along through the water with the dolphin and watching the water pass by the two of you. That water collides with the dolphin's rounded nose and spreads outward, away from the dolphin's skin. (A) Compare the water pressure on the tip of the dolphin's nose to the pressure in the freely flowing stream of water nearby. (B) Compare the water's speed on the tip of the dolphin's nose with the water's speed in the freely flowing stream.

Answer: (A) The water pressure is higher on the dolphin's nose than in the freely flowing stream. (B) The water's speed is lower (almost stopped) on the dolphin's nose than in the freely flowing stream.

Why: The onrushing water must bend outward, away from the dolphin's skin, as it encounters the dolphin's rounded nose. This outward bend involves an acceleration away from the dolphin's nose, so the water pressure on that nose must be higher than in the surrounding free stream. To conserve energy, this higher pressure and pressure potential energy must be accompanied by a decrease in speed and kinetic energy in the water at the dolphin's nose.

4. As you continue to ride along with the dolphin, you observe the water flowing around its sides. This water bends inward, toward the dolphin's skin, as it follows the dolphin's inward curving sides. (A) Compare the water pressure in the water passing very close to the dolphin's side to the water pressure in the nearby freely flowing stream. (B) Compare the speed of the water passing very close to the dolphin's side (but not in the boundary layer) to the speed of the water in the freely flowing stream.

Answer: (A) The water pressure near the dolphin's side is lower than in the freely flowing stream. (B) The water's speed near the dolphin's side is faster than in the freely flowing stream.

Why: As water passes the sides of the dolphin, it must undergo an inward bend in order to follow the dolphin's surface. That inward bend requires that the pressure near the surface be lower than far away from it. Thus the pressure near the dolphin's side is less than in the surrounding water. To conserve energy, this decreased pressure must be accompanied by an increase in speed in that near-surface water.

5. An object as large as a dolphin (about 3 meters) and traveling as fast as a dolphin (about 10 mph) should create turbulence in the water. (A) Give a rough estimate of the Reynolds number describing the water flow around a dolphin cruising at its typical speed. (B) What type of flow does that value predict?

Answer: (A) The Reynolds number is roughly 10 or 15 million. (B) That large a Reynolds number is almost always accompanied by turbulent flow.

Why: Reynolds number is equal to fluid density times obstacle length times flow speed, divided by fluid viscosity. In this case, the water's density is about 1000 kg per cubic meter, the obstacle length is about 3 meters, the flow speed is about 4.5 meters per second, and the water's viscosity is about 0.001 pascal-seconds. The Reynolds number one obtains from these values is about 13 million. Since turbulence is usually seen at Reynolds numbers of more than a few thousand, the dolphin should be awash in turbulence. However, the dolphin appears to have remarkable control over its skin surface (see discussion) so that it actively prevents the flow separations that result in turbulence. The dolphin creates almost no turbulent wake at all and can swim astonishingly fast as a result.

6. As part of its play, a dolphin enjoys leaping through the air. On occasion, it will squirt water out of its mouth while above the surface. The water is barely moving while it's in the dolphin's mouth, but it acquires a high speed as it shoots through the dolphin's lips on the way out of its mouth. What happens to the water's (A) pressure, (B) speed, (C) pressure potential energy, and (D) kinetic energy as that water travels toward the dolphin's lips.

Answer: The water's (A) pressure decreases, (B) speed increases, (C) pressure potential energy decreases, and (D) kinetic energy increases.

Why: The dolphin's mouth is acting as a nozzle. The dolphin uses its mouth muscles to pressurize the water. That water flows toward its open mouth, but experiences nozzle effects as it heads that way. As the passage gets narrower, the water's pressure drops and its speed increases. At the same time, the water's pressure potential energy is transformed into kinetic energy.

7. Whether it is buoyant or not, the dolphin can control its depth in the water by adjusting the angles of its body and fins as the water passes by. How does the horizontally moving dolphin obtain the vertical forces that it needs to either (A) lift itself upward against gravity or (B) sink itself downward against its own buoyancy?

Answer: By deflecting the water up or down as it passes by, the dolphin is able to obtain upward or downward lift forces. (A) To lift itself upward, the dolphin deflects the passing water downward. (B) To sink itself downward, the dolphin deflects the passing water upward.

Why: The dolphin effectively "flies" in the water. It pushes the passing water to the side and obtains a reaction force in the opposite direction. These lift forces can be so strong that the dolphin's buoyancy isn't particularly important anymore. The dolphin can even lift itself almost completely out of the water by pushing that water downward hard with its tail fluke.

8. During a skyward leap, the dolphin rises completely out of the water for a fraction of a second. There is even a time during which the dolphin is rising straight upward while not touching the water at all. During this period of upward motion, is there any upward force acting on the airborne dolphin and, if so, what is that upward force? (Neglect any buoyant effects due to the air.)

Answer: There is no upward force acting on the airborne dolphin.

Why: The dolphin is carried upward by its inertia alone. It is coasting upward while gravity is gradually slowing it to a stop. Eventually it ceases to rise and begins to descend.