Fluids and Conservation Laws - AP Physics 1

1. What is the formula for calculating the volume flow rate?

   $Q = Av$. Volume per time equals area times velocity.

2. What is the formula for hydrostatic pressure difference?

   $\Delta P = \rho g h$. Pressure change due to fluid column height and density.

3. State the equation for the continuity equation in fluid dynamics.

   $A_1 v_1 = A_2 v_2$. Conservation of mass: flow rate equals area times velocity.

4. State the relationship between fluid speed and pressure according to Bernoulli's principle.

   Higher speed, lower pressure. Energy conservation: kinetic energy trades with pressure energy.

5. What is the formula for buoyant force?

   $F_b = \rho V g$. Upward force equals weight of displaced fluid volume.

6. What is the Bernoulli effect?

   Pressure decreases as fluid speed increases. Application of energy conservation in moving fluids.

7. Find the pressure at a depth of $h$ in a fluid of density $\rho$.

   $P = P_0 + \rho gh$. Atmospheric pressure plus hydrostatic pressure from fluid column.

8. What property of a fluid determines its buoyant force?

   Density of the fluid. Buoyancy depends on displaced fluid's weight per unit volume.

9. What is the principle of conservation of mass in fluid dynamics?

   Mass flow rate is constant. Mass entering equals mass leaving any control volume.

10. Identify the formula for the mass flow rate in a pipe.

    $\dot{m} = \rho A v$. Mass per time flowing through cross-sectional area.

11. Which law states that pressure applied to a confined fluid is transmitted undiminished?

    Pascal's Law. Pressure changes propagate equally throughout confined fluids.

12. What is the density formula?

    $\rho = \frac{m}{V}$. Mass divided by volume occupied.

13. State Bernoulli's equation.

    $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$. Energy conservation: pressure, kinetic, and potential energy sum constant.

14. Calculate the volume flow rate for a pipe with $A = 0.1\, \text{m}^2$ and $v = 3\, \text{m/s}$.

    $Q = 0.3\, \text{m}^3/\text{s}$. Using $Q = Av = 0.1 \times 3$.

15. State the relationship between flow speed and cross-sectional area in a pipe.

    Inversely proportional. Conservation of mass requires $Av$ constant in continuity equation.

16. What is the SI unit for density?

    Kilograms per cubic meter ($\text{kg/m}^3$). Mass divided by volume in base SI units.

17. What is the term for the resistance to flow in fluids?

    Viscosity. Internal friction opposing relative motion in fluids.

18. What happens to fluid pressure as depth increases?

    Pressure increases. Weight of fluid column above creates greater pressure.

19. State the relationship between fluid pressure and area.

    Inversely proportional. Same force over larger area creates lower pressure.

20. What is Torricelli's theorem used for?

    Calculating fluid exit speed. Determines speed of fluid exiting containers under gravity.

21. Calculate the density if mass $m = 500\, \text{kg}$ and volume $V = 2\, \text{m}^3$.

    $\rho = 250\, \text{kg/m}^3$. Using $\rho = \frac{m}{V} = \frac{500}{2}$.

22. Calculate the buoyant force on a $2\, \text{m}^3$ object submerged in water ($\rho = 1000\, \text{kg/m}^3$).

    $F_b = 19600\, \text{N}$. Using $F_b = \rho Vg = 1000 \times 2 \times 9.8$.

23. What is the effect of temperature on fluid viscosity?

    Viscosity decreases with temperature. Higher temperature reduces intermolecular forces and friction.

24. What is the primary cause of viscosity in fluids?

    Internal friction. Molecular interactions resist relative motion between fluid layers.

25. State the formula derived from Torricelli's theorem.

    $v = \sqrt{2gh}$. Speed equals free-fall velocity from height $h$.

26. Determine the force exerted by a fluid on a dam with $A = 100\, \text{m}^2$ and $P = 5000\, \text{Pa}$.

    $F = 500000\, \text{N}$. Using $F = PA = 5000 \times 100$.

27. What is the formula for pressure in fluids?

    $P = \frac{F}{A}$. Force per unit area exerted by or on a fluid.

28. What is the unit of pressure in the SI system?

    Pascal (Pa). Named after Blaise Pascal, equals one newton per square meter.

29. Identify the principle that explains buoyant force.

    Archimedes' Principle. Describes upward force on objects immersed in fluids.

30. Identify the term for fluids with zero viscosity.

    Ideal fluids. Theoretical fluids with no internal friction or energy loss.

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