Fluid mechanics Flashcards
What is density?
Density is the mass per unit volume of a material, denoted by rho. Formula: rho = m / V.
What are the SI units of density?
kilograms per cubic meter (kg/m^3).
What is the SI unit of pressure?
Pascal (Pa)
Why is density a property of a pure substance?
It’s a characteristic that remains constant for a pure substance under specific conditions (e.g., temperature and pressure), like water’s 1000 kg/m^3 at 4°C.
How are density (rho) and mass (m) related when volume (V) is constant?
Density is directly proportional to mass: rho increases as m increases. Example: A brick has higher density than a sponge of the same volume due to greater mass.
How are density (rho) and volume (V) related when mass (m) is constant?
Density is inversely proportional to volume: rho increases as V decreases. Example: Popcorn has lower density than corn seeds of the same mass due to larger volume.
A large cube has twice the mass and twice the side length of a small cube with density rho. What’s the large cube’s density?
B. rho. Volume scales with side length cubed (2^3 = 8), so rho_large = (2m) / (8V) = m / (4V) = rho / 4 * 4 = rho.
What is pressure in a fluid?
Pressure is the normal force per unit area exerted by a fluid, defined as p = dF_perp / dA.
What are the SI units of pressure?
What are the SI units of pressure?
Is pressure a scalar or vector quantity?
Pressure is a scalar (no direction), but the force it exerts is a vector, perpendicular to the surface.
What is absolute pressure?
The total pressure, including atmospheric pressure. It can never be negative.
What is gauge pressure?
Generally, as temperature increases, the density of a fluid decreases.
Why don’t we feel air pressure on our hand?
Air pressure exerts equal forces on both sides of the hand, netting zero force, unlike water’s downward force.
Calculate the force of air pressure and 25L of water on a 25 cm^2 hand. (rho_water = 1000 kg/m^3, p_atm = 101325 Pa, g = 9.8 m/s^2)
Air: F = p * A = 101325 * 0.0025 = 253.3 N. (b) Water: F = m * g = (25 * 10^-3 * 1000) * 9.8 = 245 N.
How does pressure vary with depth in an incompressible fluid?
Pressure increases with depth: p2 - p1 = p_2 + rho * g * y_2 = p_1 + rho * g * y_1.
What are key tips for using p2 + rho * g * y2 = p1 + rho * g * y1?
Use in same liquid, rho is liquid density, y-axis points up, pressure equal at interfaces.
A climber’s watch reads -0.1 bar gauge pressure. What’s the absolute pressure? (1 bar = 10^5 Pa, p_atm = 1.013 bar)
0.9 bar. Absolute = gauge + atmospheric = -0.1 + 1.013 = 0.913 bar ≈ 0.9 bar.
What happens to an incompressible fluid under pressure?
Volume and density stay constant. Examples: water, oil, bricks.
how does density and pressure change in an incompressible fluid in different heights?
density: constant
pressure increases at lower depth
higher up decreases.
What happens to a compressible fluid under pressure?
Volume decreases, density increases. Examples: gases, sponges.
how does density and pressure change in a compressible fluid in different heights?
density: if you are higher it decreases. decrease in depth is and increase in density
pressure increases at lower depth
higher up decreases.(same as density)
As an air bubble rises from the ocean bottom, what happens to its volume and density?
Volume increases, density decreases. Pressure decreases, so V increases, and rho = m / V decreases.
What is Archimedes’ Principle?
The buoyant force on an object equals the weight of displaced fluid: B = rho_fluid * V_displaced * g.
definition: When a body is completely or partially immersed in a fluid, the fluid exerts an upward force (“buoyant
force”) on the body equal to the weight of the fluid displaced by the
body.
buoyant force equations
F_B = rho_fluid * V_displaced * g
F_B = w_volume of water
F_B = mg
How is buoyant force derived for a cube?
F_net = p1 * A - p2 * A = (p2 + rho * g * h) * A - p2 * A = rho * g * h * A = rho * g * V.
Which block (ice, 920 kg/m^3, or iron, 7800 kg/m^3) has greater buoyant force when submerged?
Both experience the same buoyant force. B = rho_fluid * V, same V, same fluid.
A crown and gold of equal mass are submerged. Which displaces more water?
The crown (less dense) has larger volume, displaces more water, and has greater buoyant force
What is the formula to calculate the buoyant force on a submerged object?
F_b = ρ_fluid * V_submerged * g
What are the key equations for static fluids?
Density: rho = m / V. Pressure: p = dF_perp / dA. Pressure-depth: p2 + rho * g * y2 = p1 + rho * g * y1. Buoyancy: B = rho_fluid * V_displaced * g.
atmospheric pressure
constant
absolute pressure formula
P_abs = P_gauge + P_atm
liter to cm squared conversion
litre = cm^2
litre to m^3 conversion
1 litre = 1 * 10^-3 m^3
