AP Tests are coming up soon! Let’s do some physics review.

FLUIDS KEY CONCEPTS AND PRINCIPLES:

1. Density of a fluid is given as its mass over volume; D = m/v
2. Specific gravity of a substance is the density of a substance over the density of water; for example, the density of iron is 7800 kg per cubic meter, while the density of water is 1000 kg per cubic meter; thus, the specific gravity of iron is 7800/1000 = 7.8
3. Pressure is mathematically defined as a scalar quantity given by the force per unit area. Standard pressure is given as P₀ = 1 atm or 1.013 * 10⁵ Pascals
   • Pressure in fluids is dependent on the depth (which can be given by a liquid’s volume divided by the cross sectional area of the container). The gauge pressure is then given as the density of the fluid (rho) multiplied by g, multiplied by the depth (h); P_G = 𝜌gh
   • The absolute pressure is the standard pressure added to the gauge pressure in a fluid (P_G = 𝜌_fluidgh, or the gauge pressure in air subtracted from the standard pressure (P_G = 𝜌_airgh)
4. Pascal’s principle and the Hydraulic Lift:
   • For a hydraulic press in the form of an U-shaped tube with two branches and two different cross sectional areas, the ratio of the applied force to the area of one branch is the same as the ratio of the applied force to another area of the branch: F₁/A₁ = F₂/A₂
5. Archimedes’ Principle:
   • Applicable to static fluids (fluids that do not move)
   • If an object sinks, then it keeps sinking until it reaches the bottom
   • For all submerged objects in a fluid, there is a force exerted on it by the fluid (buoyant force)
     • The buoyant force always points UPWARD
     • The magnitude of the buoyant force is given as 𝜌_fluid*V_displaced*g, or the density of the fluid multiplied by the displaced volume multiplied by the gravity
     • When an object floats, the buoyant force is equal to the force of gravity
     • When an object sinks to the bottom (and touches the bottom) of a container, the force of gravity is greater than the sum of the normal force and the buoyant force
     • When an object is completely submerged in a fluid, but stands still (because it is being suspended by an applied force), then the sum of the applied force and the buoyant force is equivalent to the force of gravity
6. Bernoulli’s Principle:
   • Deals with dynamic (or moving) fluids
   • The conditions for Bernoulli’s Principle entail low or no viscosity and a constant density throughout the fluid
   • Based on the conservation of energy, it is given as: P₁ + 𝜌₁gh + $\frac{1}{2}*\rho_1*v_1^2$ = P₂ + 𝜌₂gh + $\frac{1}{2}*\rho_2*v_2^2$
   • v is the velocity of the fluid, rho is the density of the fluid, h is the elevation, and P is the pressure
   • Spigot Hole:
     • When a fluid is filled to a height of $h_o$ and it comes out of the spigot at height $h_{spigot}$, the velocity at which it comes out is given by $v = \sqrt{(2g(h_o – h_{spigot})}$. See if you can derive this from Bernoulli’s Principle!
7. Continuity Principle:
   • The flow rate in different sections of the pipe remains the same; $V_1=V_2 = v_1A_1 = v_2A_2$, where V is the volumetric flow rate, v is the velocity of the fluid, and A is the cross sectional area

That’s the fluids review for today! Come back soon for another unit, probably physics 2 :).