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 ships float
A pascal is a newton per square meter
Buoyant force
Flow rate
Applying Bernoulli and continuity together
Hydraulic advantage
Torricelli's result
Continuity before Bernoulli
Buoyancy is a pressure difference
Float, sink or hover
Why a shower curtain pulls inward
Density of water
Short answer 1. Define or explain: Measuring density by double weighing
3 ptsShort answer 2. Define or explain: Pressure with depth
3 ptsShort answer 3. Define or explain: Gauge pressure can be negative
3 ptsShort answer 4. Define or explain: Density
3 ptsFree response
8 ptsQUALITATIVE/QUANTITATIVE TRANSLATION (Question 4, 8 points). In Scenario 1, a swimmer holds a block of mass m at rest, fully submerged in a tank of freshwater with density ρ1; when released from rest the block accelerates upward with initial acceleration a1. In Scenario 2 the swimmer holds the same block at rest in a tank of salt water with density ρ2 > ρ1; released again, the block accelerates upward with initial acceleration a2. All frictional forces are negligible.
A. Indicate whether a1 is greater than, less than, or equal to a2, and justify your answer in terms of ALL forces exerted on the block in each scenario, using qualitative reasoning beyond referencing equations.
B. For the general case of a block of mass m and volume V completely submerged in a fluid of density ρ: starting with Newton’s second law, derive an expression for the initial upward acceleration a of the block when released from rest, in terms of m, V, ρ, and physical constants, as appropriate.
C. Indicate whether the expression derived in part B is or is not consistent with the claim made in part A, and briefly justify by referencing the derivation.