Unit 8: Fluids

19 terms. Say what each one means, then open the card to check.

• Density

  Mass per unit volume, $\rho = m/V$, in kg/m³. It belongs to the material, so a small piece and a large piece of the same material have the same density.

  Example. A 0.20 m³ log with a mass of 120 kg has a density of 600 kg/m³.

• Pressure

  The force pressing perpendicular to a surface divided by the area it is spread over, $P = F/A$. Its unit is the pascal: 1 Pa = 1 N/m².

  Example. A 30 N book lying on a face of area 0.060 m² presses on the table with a pressure of 500 Pa.

• Atmospheric pressure

  The pressure from the weight of the air above, about 1.0 × 10⁵ Pa at sea level. It pushes on every surface, from every direction.

  Example. Air presses on each square centimeter of your hand with a force of about 10 N, but the push from every side balances.

• Pressure at a depth

  In a fluid at rest, the pressure a depth h below the surface is $P = P_0 + \rho g h$, where $P_0$ is the pressure at the surface; it rises steadily with depth.

  Example. In fresh water, every 10 m of depth adds about 9.8 × 10⁴ Pa, almost one more atmosphere.

• Gauge pressure

  The pressure above atmospheric pressure. For a liquid open to the air, the gauge pressure at depth h is $\rho g h$.

  Example. At the bottom of an aquarium filled 0.40 m deep, the gauge pressure is about 3.9 × 10³ Pa.

• Absolute pressure

  The total pressure: the gauge pressure plus atmospheric pressure.

  Example. Where the gauge pressure is 5.0 × 10⁴ Pa, the absolute pressure is about 1.5 × 10⁵ Pa.

• Pascal’s principle

  Push harder on a fluid that is sealed in, and the extra pressure you add shows up everywhere in that fluid, at full strength, not just where you pushed.

  Example. Pressing a car’s brake pedal raises the pressure in the brake fluid, and the same rise reaches the brake at every wheel.

• Pressure and container shape

  At one depth in a connected fluid at rest, the pressure is the same no matter how wide, narrow or oddly shaped the container is.

  Example. A tall narrow vase and a wide bowl filled with water to the same depth have the same water pressure at the bottom.

• Buoyant force

  The upward force a fluid exerts on an object in it. It arises because the fluid pushes harder on the deeper bottom of the object than on its top.

  Example. A beach ball pushed under water shoots back up because the water pushes up on it far harder than gravity pulls it down.

• Archimedes’ principle

  The buoyant force equals the weight of the fluid the object pushes aside: $F_b = \rho_{fluid}V_{disp}g$.

  Example. A rock with a volume of 0.0040 m³ held completely under fresh water feels a buoyant force of about 39 N.

• Floating

  A floating object at rest settles until the buoyant force equals its weight, so it pushes aside its own weight of fluid.

  Example. A 2.0 kg wooden duck decoy floats by pushing aside 2.0 kg of water, which is 0.0020 m³.

• Fraction submerged

  For a floating object, the fraction of its volume below the surface equals $\rho_{object}/\rho_{fluid}$.

  Example. A foam block with a density of 450 kg/m³ floats in fresh water with 45 percent of its volume below the surface.

• Average density and sinking

  An object floats if its average density is less than the fluid’s and sinks if it is greater. For a hollow object, the average includes the air inside.

  Example. A steel canoe floats because its thin steel shell and the air inside it together average far less than 1000 kg/m³.

• Apparent weight

  The weight an object seems to have in a fluid: its true weight minus the buoyant force on it.

  Example. A 60 N stone that pushes aside 25 N of water feels like only 35 N when you lift it under water.

• Ideal fluid

  A model fluid that cannot be compressed, has no viscosity (no internal friction) and flows steadily without swirling.

  Example. Water moving slowly through a wide, smooth pipe is close to ideal; thick syrup creeping through a narrow tube is not.

• Volume flow rate

  The volume of fluid passing a cross section each second, $Q = Av$, in m³/s.

  Example. Water moving at 2.0 m/s through a channel with a cross section of 0.010 m² delivers 0.020 m³, or 20 liters, each second.

• Continuity equation

  For an incompressible fluid in one pipe, the flow rate is the same at every cross section: $A_1v_1 = A_2v_2$, so the fluid moves faster where the pipe is narrower.

  Example. Where a pipe’s cross-sectional area drops to one-fifth, the water moves five times as fast.

• Bernoulli’s equation

  Along the flow of an ideal fluid, $P + \frac{1}{2}\rho v^2 + \rho g y$ has the same value at every point; it is energy conservation for each cubic meter of fluid.

  Example. In a level pipe, the water in a fast-moving stretch is at a lower pressure than the water in a slow-moving stretch.

• Speed out of a hole in a tank

  Water leaving a small hole a depth h below the open surface of a wide tank moves at about $v = \sqrt{2gh}$, the speed of a drop that has fallen a height h.

  Example. A small hole 0.45 m below the water surface squirts water out at about 3.0 m/s.