Density and pressure
7 flashcards to master this topic
Define density.
Density (ρ) is mass per unit volume. It is calculated as ρ = m/V, where m is mass and V is volume. Common units are kg/m³ or g/cm³.
Define pressure.
Pressure (p) is the force acting perpendicularly per unit area. It is calculated as p = F/A, where F is the force and A is the area. The SI unit is Pascal (Pa), which is equivalent to N/m².
Derive the formula for hydrostatic pressure (∆p = ρg∆h).
Consider a column of fluid of height ∆h, area A, and density ρ. The weight of the fluid column is mg = ρVg = ρA∆hg. The pressure difference ∆p is the weight divided by the area: ∆p = (ρA∆hg)/A = ρg∆h.
A submarine is at a depth of 50m in seawater (density 1030 kg/m³). Calculate the hydrostatic pressure acting on it.
Using ∆p = ρg∆h, where ρ = 1030 kg/m³, g = 9.81 m/s², and ∆h = 50m, we get: ∆p = 1030 * 9.81 * 50 = 505115 Pa. Therefore, the hydrostatic pressure is approximately 505 kPa.
Explain why an object submerged in a fluid experiences upthrust.
Upthrust occurs because the pressure at the bottom of the object is greater than the pressure at the top. This pressure difference creates a net upward force, known as upthrust (Archimedes' principle).
State Archimedes' principle.
Archimedes' principle states that the upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Mathematically, Upthrust = ρgV where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the fluid displaced (which is the volume of the submerged object).
A stone of volume 0.01 m³ is fully submerged in water (density 1000 kg/m³). Calculate the upthrust on the stone.
Using F = ρgV, where ρ = 1000 kg/m³, g = 9.81 m/s², and V = 0.01 m³, the upthrust is: F = 1000 * 9.81 * 0.01 = 98.1 N.
Ready to test yourself?
Practice with MCQ questions to check your understanding of Density and pressure.
Take QuizStudy Mode
Rate each card Hard, Okay, or Easy after flipping.