Definition of pressure: Force Area ysics Courseware ysics I Bernoulli Hydrostatics equation: B A Bernoulli s equation: roblem.- In a carburetor (scematically sown in te fiure) calculate te minimum speed of te air at te nozzle so te difference in pressure wit te fuel reseroir is at least,500 pascals. [Take te density of air as.9 k/m ] Solution: Usin Bernoulli s equation we et: p p,500 And wit te alues of te problem: 48. m/s.9 roblem.- Te pipe in te fiure is transportin oil (density 850 k/m ). Te elocity at point is 5m/s, but at point it is 0m/s. Calculate te difference in eit in te two open tin tubes Solution: First we can calculate te pressure difference in pascals between points &. Usin Bernoulli s equation:
0 5 850,875 pascals And now we use ydrostatics to find :,875,875.8 m 850 9.8 roblem.- erfume in a bottle as a density of 955 k/m and its leel is 0.05m below te nozzle as sown in te fiure. Calculate te minimum speed of te air, so te liquid will reac te nozzle. [For te density of air use air.9k / m ] Solution: Te difference in pressure needed for te liquid to reac te nozzle can be calculated usin te ydrostatic equation: A B 955 9.8 0.05 4pascals Now, to find te elocity tat produces tis cane in pressure we need to compare points and : But te eit is te same for points and and te elocity at point is zero (far from te nozzle), so: 4 9 m/s. 9
roblem 4.- A itot tube is an instrument used to measure airspeed of an aircraft. Calculate te cane in pressure read by te instrument if te airspeed is 05 m/s. [take te density of air at tese conditions as 0.95k/m ] Solution: Usin Bernoulli s equation: we et If 05m/s and /.95 0 m k ten 05 0.95 5,00 pascals roblem 4a.- A itot tube is an instrument used to measure airspeed of an aircraft. Calculate te speed if te pressure difference read by te instrument is 7,500 pascals. [take te density of air at tese conditions as 0.95k/m ] Solution: Usin Bernoulli s equation: we et ten 0.95 7500 5 m/s
roblem 5.- Te fiure sows a so called Venturi tube wic is used to measure as flow. Te U-saped tube section contains mercury and te leels are equal because tere is no flow rit now. Use your knowlede of Bernoulli s principle to predict wat will appen to te mercury leels wen te as flow starts. Solution: Te fluid will flow faster in te small cross section area, so te pressure will drop at tat point. Te mercury inside te tube will rise on te rit and drop on te left. roblem 5a: Te Venturi tube sown in te fiure as a restriction in te cross section, so te speed of te air flow at point is 0 m/s, wile te speed at point is 0 m/s. Calculate te difference in te leel of mercury under tese conditions. [Take te density of air.9k/m ][ torr pascals] Solution: First we can calculate te pressure difference in pascals and ten conert to torr. Usin Bernoulli s equation: 0 0.9 94 pascals torr Conertin to torr: 94 pascals.45 torr pascals So.45 mm
roblem 5b.- Te Venturi tube sown in te fiure as a restriction in te cross section, so te speed of te air flow at point is 5 m/s, wile te speed at point is 0 m/s. Calculate te difference in te leel of water in te U-tube under tese conditions. [Take te density of air.9k/m and water000k/m ] Solution: First we can calculate te pressure difference in pascals. Usin Bernoulli s equation: 5 0.9 80.6 pascals Now we can find te alue of water 80.6 000 9. 8 0.008 m So 8. mm roblem 6: Te airspeed on te top surface of a win is 05m/s, but only 95m/s on te bottom surface. Te win as an area of 5m. Use Bernoulli s principle to calculate te net force tryin to lift te win. Inore oter mecanical effects suc as iscosity dra. Take te density of air as.0k/m Solution: Bernoulli s principle: constant says tat you can trade speed for pressure. Wen te wind blows aboe a surface te pressure drops, so tere will be a net force ien by te area of te win times te difference in pressure: ( ) Force (Area) so te force is: F (5) (.0)(05-95 ) 8,000 N
roblem 7.- A itot tube is an instrument used to measure airspeed of an aircraft or fluid flow in pipes. In te followin scematic, te mercury is leeled because tere is no flow. Indicate wat will appen to te mercury wen flow starts and ie a sort rationale of your answer. Solution: Te aerae speed of molecules tat are at point a is zero (tey cannot flow anywere) wile te ones a point b ae nonzero aerae elocity, so te pressure at a is larer tan at b and te mercury will moe to te position sown. roblem 7a.- A itot tube is an instrument used to measure airspeed of an aircraft or fluid flow in pipes. In te followin scematic, te mercury is leeled because tere is no air flow. Wen te flow starts te leel on te rit oes up 0.5mm (and te leel on te left oes down 0.5 mm). Calculate te speed of te air if te density of air is.9k/m and te density of mercury is,600 k/m. Solution: We write Bernoulli s equation for points and : Te elocity at point is zero as discussed in class. Te eits are te same ( ), so we can eliminate tem from te equation leain: ( ) But te pressure difference can be calculated usin te alue of H: H,600k / m (9.8m / s )( 0 m) Mercury. pascals (. pascals) So te elocity of te air is: 4.4 m/s.9k / m
roblem 7b: A itot tube is an instrument used to measure airspeed of an aircraft or fluid flow in pipes. In te followin scematic, te mercury is initially leeled because tere is no flow. Calculate te difference in leel wen te speed of te flow of air is 0.5 m/s. [Take te density of air.9k/m ][ torr pascals] Solution: Usin Bernoulli s equation: a Takin into account tat a 0 and a b we et: b a a b b a b b b a b b (.9)(0.5 ) 7 pascals a In mm of mercury tis is: 0.5 mmh b roblem 8.- How would you use Bernoulli s principle to calculate te force on a flat roof produced by wind of speed? Write te equation(s) tat you would use. Solution: Bernoulli s equation can be used to calculate te cane in pressure: constant and ten find te force by multiplyin by area: F A
roblem 8a.- Te wind is blowin at a speed of 5 miles/our oer a flat roof of area 95m. Use Bernoulli s principle to calculate te net force tryin to lift te roof. Solution: Bernoulli s principle: constant says tat you can trade speed for pressure. Wen te wind blows aboe a roof te pressure drops outside, so tere will be a net force ien by te area of te roof times te difference in pressure: Force (Area) we need te speed in m/s: mile 609m 5.m/s 600s mile So te force is: Force (95m ) (.9k/m )(.m/s) 7,650 N roblem 9.- You want water to reac a eit of H meters wit a fire ose. Calculate te minimum aue pressure in te mains to do tis. Assume te speed of te water in te mains to be neliible and density water 000k / m Solution: Notice tat te speed in te mains and te speed at te maximum eit are bot zero, so we can use te ydrostatic equation: 000 9.8,000 pascals A B
roblem 0.- rairie dos built te followin arcitecture. Indicate in wat direction air will flow in te tunnel And explain wy. Solution: Bernoulli s equation constant, says tat you can trade speed for pressure. Wen te wind blows aboe te top of te mound, te pressure drops, so tere will be a draft as sown below: