Fluid mechanics practice questions.

A track cyclist doubles her speed along the back straight while holding the same riding position. How does the air resistance acting on her change?

• It approximately doubles
• It approximately quadruples
• It is unchanged, because her frontal area has not altered
• It approximately halves, because she spends less time in the air stream

Answer: It approximately quadruples

Drag rises approximately with the square of velocity, so doubling the speed multiplies the resistive force by about four. This is why aerodynamic gains matter far more to a track sprinter than to a slow recreational rider.

A speed skater moves from an upright position into a low crouch with a flat back. Which component of the resistive force is reduced most by this change of shape?

• Form drag, because the low-pressure wake behind her is reduced
• Surface drag, because the area of suit in contact with the air falls
• Wave drag, because fewer waves are produced at the surface of the ice
• Friction between blade and ice, because the contact area is reduced

Answer: Form drag, because the low-pressure wake behind her is reduced

Streamlining changes the shape of the body, so it acts on form drag, which is caused by the pressure difference between the front of the skater and the turbulent wake behind her. The classic error is to credit streamlining with reducing skin friction, which depends on surface texture and wetted area instead.

After a tumble turn a swimmer stays about 0.5 m below the surface for the first few metres of the underwater phase. Which resistive component is largely avoided while she remains submerged?

• Surface drag, which arises from friction between the skin and the water
• Form drag, which arises from the pressure difference around the body
• Wave drag, which is created at the boundary between water and air
• Drag from the turbulence created by the swimmer in the next lane

Answer: Wave drag, which is created at the boundary between water and air

Wave drag is generated only where the body disturbs the water-air interface, so it disappears once the swimmer is deep enough for the bow wave not to form. Surface and form drag continue to act underwater, which is why the underwater phase is still shortened by a poor streamline position.

A rowing eight is timed over the same course under different conditions. Which combination would give the largest drag force acting on the boat?

• Lower velocity together with a smoother, freshly waxed hull surface
• Greater velocity and a smaller frontal area
• Lower velocity and a greater frontal area
• Greater velocity and a greater frontal area

Answer: Greater velocity and a greater frontal area

Drag rises both with the velocity of the boat relative to the water and with the cross-sectional area presented to the flow, so here the two changes reinforce each other. Lowering the velocity together with a smoother hull lowers both contributions, while the two remaining combinations pair one drag-raising with one drag-lowering change, so their net effect is not determined.

Water passing over the hull of a racing kayak breaks into swirling eddies behind the cockpit. Which statement about this flow is correct?

• The flow is now turbulent, which increases drag on the hull
• The flow is now laminar, which increases drag on the hull
• The flow is now turbulent, which reduces the pressure difference across the hull
• The flow is unaffected, because eddies form only behind the boat

Answer: The flow is now turbulent, which increases drag on the hull

Eddies mark the change from smooth layered flow to turbulent flow, and the turbulent wake lowers the pressure behind the hull, which raises form drag. Laminar flow is the smooth, layered case and is associated with the lower drag, not the higher.

A sea kayaker paddles the same loaded kayak out of a freshwater estuary into the denser water of the open sea. What happens to the kayak once it is floating at rest there?

• It sits lower in the water, because the denser sea water presses down harder on the hull and on the deck
• It floats at the same depth, because the upthrust on a floating body always equals its weight
• It sits higher in the water, because a smaller volume must be displaced to balance the same weight
• It sits higher, because the upthrust on the kayak is now greater than the weight of the kayak

Answer: It sits higher in the water, because a smaller volume must be displaced to balance the same weight

A floating body displaces its own weight of fluid, so in denser sea water that same weight is balanced by a smaller displaced volume and the hull rides higher. The upthrust itself is unchanged, since it still equals the weight, which is why the answer is about the volume displaced rather than about a larger force.