Fluid mechanics(theory questions) Flashcards
Which are fluids at room temperature and atmospheric pressure: air, mercury, water, glass?
Air (gas), mercury (liquid), water (liquid). Glass is an amorphous solid, not a fluid.
How does air density vary with altitude?
Decreases exponentially with altitude if temperature is constant; varies with temperature changes in reality.
Floating ice and a glacier of equal volume melt into a lake. Which raises the level more?
Glacier. Floating ice already displaces water; glacier adds full volume
How does pressure relate to a knife’s sharpness and cutting ability?
p = F / A. Sharper knife has smaller A, increasing p, enhancing cutting.
Atmospheric pressure exerts ~10 tons on you sunbathing. Why can you get up?
Pressure acts equally all around, netting zero force unless in a vacuum.
How do sandbags stop water leaking under a levee?
Water in sandbags rises to river level, equalizing pressure across the leak.
Why do fluid levels equalize in a manometer open to atmosphere, even with different tube diameters?
Pressure at same depth is equal (p = rho * g * h), independent of tube area.
Why more force to pull a plug in a full tub? Contradict Archimedes’?
Water weight adds pressure (Pascal’s). No—Archimedes’ is buoyancy, not pressure.
Does atmospheric pressure add to gas pressure in a rigid tank? In a balloon?
No for rigid tank (fixed volume); yes for balloon (expands).
Does a ship float higher in salt water than fresh water?
Yes. Salt water’s higher rho means less volume displaced for same buoyant force.
Why is fluid velocity greatest where streamlines are closest?
Continuity: A * v = constant. Closer streamlines mean smaller A, higher v.
Why does a fountain stream broaden rising, but a faucet stream narrow falling?
Continuity: v * A = constant. Fountain slows (gravity), A grows; faucet speeds up, A shrinks
How does a Venturi tube’s narrow segment enhance entrainment?
Continuity speeds flow, Bernoulli lowers pressure, drawing in fluid.
Is there a limit to how high an entrainment device can raise fluid?
Yes, pressure energy (P) becomes potential (rho * g * h), kinetic energy limits height.
Why do roofs lift off in cyclones or buildings explode in tornadoes?
Bernoulli: fast wind lowers outside pressure; higher inside pressure lifts roof.
How can water exit a nozzle with pressure below atmospheric?
Bernoulli: kinetic energy (1/2 * rho * v^2) overcomes pressure difference.
What are three forms of energy in Bernoulli’s equation?
Potential (rho * g * h), kinetic (1/2 * rho * v^2), pressure (P).
Why paddle near shore upstream, middle downstream in a canoe?
Shore water slower (friction). Upstream: less resistance. Downstream: faster midstream helps.
In a constricted artery, where is blood speed greatest? Why higher resistance?
At constriction (A * v = constant). Resistance from smaller A and turbulence.
Volume of 1 troy ounce (31.103 g) of gold (rho = 1.93 x 10^4 kg/m^3)?
V = m / rho = 0.031103 / 19300 = 1.610 x 10^-6 m^3 = 1.610 cm^3.
Mass of 2.00 L breath (rho_air = 1.29 kg/m^3)? Effect on body density?
m = rho * V = 1.29 * 0.002 = 0.00258 kg = 2.58 g. Body volume up, density down (air less dense).
Radius of mug holding 375 g coffee (rho = 1000 kg/m^3) at 7.50 cm depth?
V = m / rho = 0.375 / 1000 = 0.000375 m^3. A = V / h = 0.00005 m^2. r = sqrt(A / pi) = 0.0399 m = 3.99 cm.
Trash compacted to 0.350 original volume. Density factor increase?
rho_new = m / (0.350 * V) = rho_old / 0.350 = 2.86 * rho_old.
Density of 18-karat gold (18 parts gold, 5 silver, 1 copper by mass)?
Weighted avg: (18/24 * 19.3 + 5/24 * 10.5 + 1/24 * 8.92) = 15.6 g/cm^3.
Height of mercury column for 1 atm (1.013 x 10^5 Pa, rho = 1.36 x 10^4 kg/m^3)?
p = rho * g * h. h = 1.013 x 10^5 / (1.36 x 10^4 * 9.8) = 0.760 m = 760 mm.
Dam (H = 12 m, W = 10 m, rho = 1000 kg/m^3). (a) Net force? (b) Why thicker at bottom?
F = 1/2 * rho * g * W * H^2 = 7.06 x 10^6 N. (b) p = rho * g * h increases with depth.
Height of water manometer for 300 mm Hg (rho_Hg = 1.36 x 10^4 kg/m^3)?
p = rho_Hg * g * 0.3 = 1000 * g * h. h = 0.3 * 13600 / 1000 = 4.08 m.
Pressure in hydraulic system from example (force calc) in atm?
Given as 251 atm (complex calc from text example).
Cork (d = 2 cm) pounded with 120 N breaks jug bottom (d = 14 cm). Extra force?
p = 120 / (pi * 0.01^2) = 3.82 x 10^5 Pa. F = p * (pi * 0.07^2) = 5.76 x 10^3 N.
Prove work input = work output in hydraulic system (no friction)?
A1 * d1 = A2 * d2 (constant volume). F1 * d1 = F2 * d2 since F2 / F1 = A2 / A1.
Body (rho = 995 kg/m^3) in (a) fresh water (1000 kg/m^3), (b) salt water (1027 kg/m^3). Submerged fraction?
(a) 995 / 1000 = 0.995. (b) 995 / 1027 = 0.969.
Iron (390 g air, 350.5 g submerged, rho = 7860 kg/m^3). (a) Fluid displaced? (b) Volume? (c) Fluid rho?
(a) 39.5 g. (b) V = 0.390 / 7860 = 0.00005 m^3 = 50 cm^3. (c) rho = 0.0395 / 0.00005 = 790 kg/m^3 (ethyl alcohol).
Woman floats with 4% above water. (a) Density? (b) % above in seawater (1027 kg/m^3)?
(a) 0.96 * 1000 = 960 kg/m^3. (b) 1 - 960 / 1027 = 0.0634 (6.34%).
Cork (rho = 240 kg/m^3). (a) Submerged fraction? (b) With 10 g cork + 20 g magnet? (c) In ethyl alcohol (806 kg/m^3)?
(a) 240 / 1000 = 0.24. (b) (10 + 20) / (1000 * V) = 0.72, V = 0.0000417 m^3. (c) Yes, 30 / 806 < 1.
Gasoline flow rate (cm^3/s) for car at 100 km/h, 10 km/L?
Q = (100 / 10) / 3600 = 0.00278 L/s = 2.78 cm^3/s.
River (300,000 L/s) narrows to 20 m wide, 20 m deep. (a) Speed? (b) Widens to 60 m, 40 m?
(a) v = 0.3 / (20 * 20) = 0.75 m/s. (b) v = 0.3 / (60 * 40) = 0.13 m/s.
Hose (d = 9 cm) carries 80 L/s. (a) Speed? (b) Flow rate in m^3/s? (c) Salt water effect?
(a) v = 0.08 / (pi * 0.045^2) = 12.6 m/s. (b) 0.0800 m^3/s. (c) No, Q and v independent of rho.
