Fluids unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Why faster flow means lower pressure
Assumptions in Bernoulli's equation
Bernoulli's terms are energies per unit volume
Fraction submerged
Density of water
Why a steel ship floats
Applying Bernoulli and continuity together
Density
Gauge vs absolute pressure
A pascal is a newton per square meter
Volume flow rate
Ideal fluid
Short answer 1. Define or explain: Torricelli's result
3 ptsShort answer 2. Define or explain: Buoyancy is a pressure difference
3 ptsShort answer 3. Define or explain: Bernoulli's equation
3 ptsShort answer 4. Define or explain: Floating condition
3 ptsFree response
8 ptsTwo solid spheres have the same volume V but different masses, with m₁ < m₂. Both are held completely submerged at the same depth in a tank of water of density ρ and then released from rest. All frictional and drag forces are negligible.
A. Indicate whether the magnitude of the buoyant force exerted on sphere 1 is greater than, less than, or equal to that exerted on sphere 2. Justify your answer in terms of the forces exerted on each sphere, using qualitative reasoning beyond referencing equations.
B. Starting with Newton’s second law, derive an expression for the magnitude of the initial acceleration of a sphere of mass m and volume V released from rest while fully submerged in a fluid of density ρ. Express your answer in terms of m, V, ρ and physical constants.
C. Indicate whether the initial acceleration of sphere 1 is greater than, less than, or equal to that of sphere 2, and justify how your answer is consistent with the expression you derived in part B.