[01] PROBLEM SOLVING - FUNDAMENTALS OF AERODYNAMICS

Calculate the pressure, density and temperature at 11km and 15km altitudes in the standard atmosphere.

T = 216.5 K

P = 22524.74 Pa

p = 0.362 kg/m^3

T = 216.5 K

P = 11970.50 Pa

p = 0.193 kg/m^3

Find the pressure and Temperature at an altitude where the density is 0.168 kg/m3 in Standard atmosphere.

T = 216.5 K

P = 10244 Pa

On a hot day, the measured temperature and pressure are 38°C and 29.0 in Hg, respectively. Calculate the density and the density ratio.

p = 1.100 kg/m^3

density ratio = 0.898

An altimeter reads 11,200 ft when the temperature is 39°F. What is the air density and what is the standard altitude?

p = 0.001622 slugs/ft^3

h = 12488.44 ft

Calculate the pressure, density and temperature at 25,000 ft and 60,000 ft altitudes in the standard atmosphere.

𝑃25,000𝑓𝑡 = 785.50 𝑙𝑏/𝑓𝑡2

ρ25,000ft = 0.001065 slug/ft3

𝑇 = 429.85 °𝑅

𝑃60,000𝑓𝑡 = 149.27 𝑙𝑏/𝑓𝑡2

ρ60,000ft = 0.000223 slug/ft3

𝑇 = 390.15 °R

At a certain altitude, a standard altimeter reads 3,000 meters. If the density altitude is 2,500 meters, find the true temperature.

T = 255.18 K

A pipe is tapering in size, diminishing by 0.1 square ft per foot run. What is the change in velocity per meter run where the pipe is 4 square ft in cross section? If the velocity there is 90 ft per second, is the velocity increasing or decreasing?

𝑑𝑉/𝑑𝑆 = 2.25 𝑓𝑝𝑠 𝑝𝑒𝑟 𝑓𝑡 , 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔

A circular pipe, 100 ft long tapers from 3 ft in diameter at one end to 2 ft in diameter at the other. Fluid is flowing from the bigger toward the smaller. What is the rate of increase in velocity at the entrance if the velocity there is 80 ft per second?

𝑑𝑉/𝑑𝑆 = 0.444 𝑓𝑝𝑠 𝑝𝑒𝑟 𝑓t

Air having the standard sea level density has a velocity of 100 fps at a section of a wind tunnel, at another section having an area half as great at that at the first section the flow velocity is 400mph. What is the density at the second section?

0.417 kg/m^3

Water is flowing through a smooth pipe whose diameter is decreasing. At one location, the diameter is 12 cm. If the velocity there is 10 meter per second. Find the mass flow rate. At a station further down the pipe, the diameter is 4cm. Find the velocity at this section.

m = 113.1 kg/s

V2 = 90 m/s

A horizontal pipe, 1ft in diameter, tapers gradually to 8 in. in diameter. If the flow is 500 cu ft of water per minute, what is the difference between the pressures at the two sections?

𝑃𝐴 - 𝑃𝐵 = 443.63𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓�

Water flows through a horizontal pipe at a velocity of 50 ft per second. Owing to the pipe gradually expanding to a larger size, the velocity decreases to 35 ft per sec. What is the difference between the pressures at two points

P𝐵 - 𝑃𝐴 = 1,236. 75 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓t

The diameter of a horizontal tube is 4 in., in which tetrabromoethane (spec. grav.=0.3) is flowing at the rate of 0.50 cu ft per sec. The pressure is 30 lb per sq in(gage). If the tube gradually decreases to 3 in. in diameter, what is the pressure there?

𝑃𝐵 = 6,416.16 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞𝑓t

Alcohol (s.g.=0.80) is flowing through a horizontal pipe, which is 10 in. in diameter with a velocity of 40 feet per second. At a smaller section of the pipe, there is 6 lb per sq. in. less pressure. Assuming that the flow is smooth. What is the diameter there?

𝑑𝐵 = 0.73 𝑓𝑡 𝑜𝑟 8.76 𝑖𝑛.

Air is flowing horizontally at a speed of 100mph through a duct 4 sq ft in cross section. The duct gradually narrows down to a throat section. If a U tube shows a difference in pressure between the throat and main section of 7 in of water, what is the cross sectional area of the throat? (Assume that the air is non-compressible and has a density of 0.002377 slugs per cu ft.).

𝐴𝐵 = 2.57 𝑠𝑞 𝑓t

A horizontal water pipe is reduced in size from 18in. in diameter at point A to 6 in. in diameter at point B. The flow in the pipe is 10 cu ft. per sec, and the pressure at A is 20 lb. per sq. in. (gage). If it is assumed that there is no loss in energy due to friction, what is the pressure at B?

𝑃𝐵 = 2,511.85 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓𝑡 or 17.44 lb/in^2

A horizontal water pipe is reduced in size from 18 in in diameter at point A to 6 in in diameter at B. The flow in the pipe is 10 cu ft per sec, and the pressure at A is 20 lb per sq in. If it is assumed that there is no loss in energy due to friction, what is the pressure at B?

PB = 395.72 lb/ft^2

A horizontal pipe line enlarges from a diameter of 6in at point A to a diameter of 12in at point B. The flow of water is 20 cu ft per sec, and the pressure at A is 10 lb per sq in. What is the pressure at B?

PB = 10872.78 lb/ft^2

Air flows through a horizontal pipe at the rate of 3,000 cu ft. per sec. If the pressure is 30 lb per sq. in. (gage) where the diameter is 3 ft., what is the pressure where the diameter is 2 ft.?

𝑃𝐵 = 5,567.10 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓t

Water flows through a horizontal pipe at the rate of 800 gal per min. What is the difference in pressure between a point where the diameter is 2 in. and a point where the diameter is 1 in.?

𝑃𝐴 - 𝑃𝐵 = 96,856.38 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓𝑡 𝑜𝑟 672.61 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑖n

The diameter at section (1) is 0.3m. The diameter at section (2) is 0.15m. What is the flow rate of a substance (sp. gr. = 0.85) if the pressure between sections (1) and (2) is 12.7 cm Hg?

𝑄 = 0.115 𝑐𝑢 𝑚𝑒𝑡𝑒𝑟 𝑝𝑒𝑟 𝑠𝑒𝑐

Consider a low-speed subsonic wind tunnel with a 12/1 contraction area ratio for the nozzle. If the flow in the test section is at a standard sea level conditions with a velocity of 50 m /s, calculate the height difference in a U-tube mercury manometer with one side connected to the nozzle inlet and the other to the test section. 𝜌𝐻𝑔 = 1.36 𝑥 103 𝑘𝑔 𝑚3

𝛥ℎ = 0.114 m

A Venturi tube narrows down from 4 inches in diameter to 2 inches in diameter. What is the rate of flow of water if the pressure at the throat is 2 lb per sq in less than at the larger section?

𝑄 = 0.388 𝑐𝑢 𝑓𝑡 𝑝𝑒𝑟 𝑠𝑒c

A venturi tube is 6 inches in diameter at the entrance, where the pressure is 10 lb per sq in. (gage). The throat is 4 inches diameter; there the pressure is 6 lb sq in. (gage). What is the flow of water?

𝑄 = 2.37 𝑐𝑢 𝑓𝑡 𝑝𝑒𝑟 𝑠𝑒𝑐.

An airplane is flying at sea level at 100mph. What is the difference between impact and static pressure?

Pt - Ps = 25.56 lb/ft^2

An airplane is flying at sea level at airspeed of 160knots. What is the difference between impact and static pressure?

Pt - Ps = 4157.72 N/m^2

An airplane is flying at 10,000ft altitude. The difference between impact and static pressure is 0.25 lb per sq in. What is the airspeed in knots?

V = 120 knots

A low speed airspeed indicator reads 200 mph when the airplane is flying at an altitude at which the altimeter reads 6000 ft. While the ambient temperature is found to be 30°F. Calculate the true speed.

V = 217.06 mph

Air at standard pressure and temperature has a density of 1.225𝑘𝑔/𝑚3 ,if the air is compressed adiabatically to 3 atm, what are the temperature, density and specific weight?

𝑤2 = 26.33 𝑁/𝑚3 ,

p2 = 2.685 𝑘𝑔/𝑚3 ,

T2 = 394.20 K

Consider a Venturi with a throat-to-inlet area ratio of 0.8 mounted in a flow at standard sea level conditions. If the pressure between the inlet and the throat is 335 Pa, calculate the velocity of the flow at the inlet

V1 = 31.18 m/s

Air at standard pressure and temperature is permitted to expand adiabatically to ½ atm pressure, what are the density and the temperature?

ρ2 = 0.747 𝑘𝑔/𝑚3

𝑇2 = 236.26 K

Air at standard pressure and temperature is adiabatically compressed to 50 lb per sq in gage pressure. What is the temperature?

𝑇2 = 792.59°R

Air at standard pressure and temperature is permitted to expand adiabatically until it is one-half standard density. a) What is the pressure? b) What is the temperature?

𝑃2 = 38,395 𝑃𝑎 , (b) 𝑇2 = 218.26 K

Find the speed of sound in air at standard sea level condition

𝑉𝑎 = 340.26 𝑚/𝑠

Find the speed of sound in air at 7,000 ft. altitude in the standard atmosphere

𝑉𝑎 = 1,089.57 𝑓𝑡/𝑠𝑒c

Find the speed of sound when the barometric pressure is 8.88 in. Hg and the density is 0.000902 slug per cu ft.

𝑉𝑎 = 987.48 𝑓𝑡/s

What is the speed of sound in air at standard temperature, 59 deg F.

𝑉𝑎 = 1,116.8 𝑓𝑡/s

In an undisturbed airstream, where the pressure is 14.7 lb per sq in and the temperature is 59°F, The velocity is 520 ft per sec where the velocity is 600 ft per sec what is the local pressure?

𝑃2 = 96,312.79𝑃a

In an undisturbed airstream, the pressure is 101325 Pa, the density is 1.225 𝑘𝑔 𝑚3 and the speed is 160𝑚/𝑠 . Find the velocity if the pressure is 90000Pa.

𝑉2 = 212.36 𝑚/s

In an undisturbed airstream, where the pressure is 14.7 lb per sq in and the temperature is 59°F, The velocity is 520 ft per sec. Where the velocity is 600 ft per sec., what is the local pressure?

𝑃 = 2,012.23 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓t

In an undisturbed airstream, where the pressure is 14.7 lb per sq in and the temperature is 59°F, The velocity is 550 ft per sec. What is the velocity where the pressure is 13.9 lb. per sq.in.?

𝑉 = 633.83 𝑓𝑡/𝑠𝑒c

A 12 inches by 6 inches Venturi meter is located in a horizontal water line. If the pressure gages read 30 lb per sq in. and 16 lb per sq in., what is the flow?

𝑄𝐻2𝑂 = 0.2602 𝑚3/s

An airplane is flying at standard sea level conditions at 45 meters per second. What is the difference between total and static pressure?

𝑃𝑡 − 𝑃 = 1,240.31 𝑃a

An airplane is flying at standard sea level conditions at airspeed of 75 meters per second. What is the total pressure?

𝑃 = 104,770.31 𝑃a

An airplane is flying at standard sea level, the difference between total and static pressure is 1,750 Pa. What is the airspeed in meters per second?

𝑉 = 53.45 𝑚/s

A uniform current of air with a speed of 100 ft per sec. flows around a circular cylinder at a distance from the cylinder the pressure is atmospheric. What is the pressure at a point on the surface of the cylinder located that a radial line through the point makes an angle of 15° with the direction of airflow?

𝑃 = 2,125.50 𝑙𝑏/𝑓𝑡2

For the flow in the above problem, what is the pressure on the cylinder surface at a 90 deg. arc from the direction of airflow?

note: A uniform current of air with a speed of 100 ft per sec. flows around a circular cylinder at a distance from the cylinder the pressure is atmospheric. What is the pressure at a point on the surface of the cylinder located that a radial line through the point makes an angle of 15° with the direction of airflow?

𝑃 = 2,081.14 𝑙𝑏 𝑝𝑒𝑟 𝑠𝑞 𝑓t

What is the pressure at 45° from the direction of air flow?

𝑃 = 2,104.92 𝑙𝑏/𝑓𝑡2

𝑃 = 2,104.92 𝑙𝑏 𝑓𝑡2

θ = 30°

A cylinder 30 inches diameter rotates in an airstream of 70mph. It develops 40 lb per ft of length. What is the rotational speed?

𝑁 = 2.66 𝑟𝑒𝑣/𝑠𝑒c

A cylinder 1.22m in diameter and 3.5m long is rotating at 100rpm in an airstream of 18m per sec. Determine the total lift of the cylinder at standard sea level conditions

Lt = 1889.49 N

Two plates, one having 6 ft. span and 3 ft. chord, the other having 9ft. span and 6 ft. chord, are placed in different airstreams. The freestream velocity for the smaller plate is 100ft/sec. It is found that the total skin-friction drag for the two plates is the same. Find the airspeed for the larger plate. Assume laminar flow at standard sea level conditions.

𝑉2 = 60.57 𝑓𝑡/𝑠𝑒c

Connsider the stabilizer on a light airplane as a flat plate for the purpose of determining its skin-friction drag. If the transition RN is 750,000, what is the skinfriction drag of a rectangular stabilizer having a span of 1.83 m and a chord of 0.91 m at a speed of 44.7 meters per second? Assume standard sea level conditions

𝐷𝑓 𝑡𝑜𝑡𝑎𝑙 = 11.65 𝑁

An airplane is flying at a density altitude of 15,000ft. At an ambient temperature a -39ᵒF. If the wing chord is 6ft and the equivalent airspeed is 200knots. What is the overall Raynolds number of the wing?

RN=12,091,834.14

Find the Reynold Number for an airplane wing 4ft chord, moving at 130mph through standard atmosphere

RN=4,850,932.14

Find the Reynold Number for an airplane wing with 3ft 6inches chord moving at 180mph through standard air.

RN=5,876,988.12

Find the Raynold Number for an airplane wing, 4ft chord, moving at 150mph. Air is +40°C, barometer,21in Hg.

RN=3,388,685.41

Find the velocity at which test should be run in a wind tunnel on a model wing of 4in chord in order that the Reynold Number shall be the same as for a wing with 4 ft chord at 100mph. Air under standard conditions in both cases

V1 = 1,212.15mph

In a variable density wind tunnel, what pressure should test be run on a model with a 3in. chord, air velocity being 60mph in order that the Raynold Number shall be the same as for the full size wing of 4ft chord, moving at 100mph through the air? Air temperatures are the same in each case.

26.67atm

What is the total force of a 45-mph wind on a hangar door 40 ft by 25ft?

𝐹 = 6,626.70 𝑙𝑏

An automobile windshield is 40 in. wide by 15 in. high and is vertical. What is the force against the windshield at 60 mph?

𝐹 = 49.09 𝑙b

What is the force against the side of a building 70ft. long and 40 ft. high in a 90 - mph wind?

𝐹 = 74,218.99 𝑙b

What force is required to push a flat plate 3 ft. by 2 ft. at a speed of 35 ft/s in a direction perpendicular to its surface?

𝐹 = 11.18 𝑙b

A stream of air 60 ft. wide and 8 ft. high is moving horizontally at a speed of 100 mph. What force is required to deflect it downward 10 deg without loss in speed.

𝐹 = 4,278.18 𝑙𝑏

A stream of air 60 ft. wide and 8 ft. high is moving horizontally at a speed of 75mph. What force is required to deflect it downward 8 deg without loss in speed

𝐹 = 1,926.06 𝑙𝑏

A stream of air 50 ft wide and 10 ft high is moving horizontally at a speed of 60mph. What is the magnitude of these force required to deflect it movement 4°downward without loss in speed?

FH = 22.42lb

FV=642.02lb

A stream of air 72 sq ft in cross section is moving horizontally at a speed of 100mph. What force is required to deflect it downward 10° without loss in speed?

F=641.76 lb

A stream of air 100sq.ft. in cross section is moving horizontally at a speed of 150mph. It strikes tangentially against the interior wall of semi-circular cylinder so that it is deflected through 180°. What is total force against the cylinder?

F=23,009.36lb

An airplane is flying at an altitude of 3,500m at an airspeed of 300 m/s. Find the critical speed, critical pressure and critical pressure coefficient.

𝑉𝑐𝑟 = 322.32 𝑚/𝑠

𝑃𝑐𝑟 = 59,981.66 𝑃𝑎

𝐶𝑃𝑐𝑟 = −0.146

What is the critical value of the pressure coefficient for an airplane flying at 500 knots in air at 25 deg F?

Cpr=-0.488

For an airplane flying at 270 meters per second at 25, 0000 ft. attitude, find the critical value of the pressure coefficient.

𝐶𝑃𝑐𝑟 = −0.254

An airfoil has a lift-curve slope of 6.3 per radian and angle of zero lift of -2 deg. At what angle of attack will the airfoil develop a lift of 140lb/ft at 100mph under standard sea level conditions? Assume c = 8ft.

𝛼 = 4.22 𝑑𝑒𝑔.

An Airplane is flying at 480mph at an altitude of 30,000ft.What is the critical Velocity?

Vcr = 952.70 ft/s

An Airplane is flying at 500knots in air at -50°F. What is the critical Velocity?

Vcr=969.35 ft/s

NACA 4412, c=100cm, find the camber, position of camber and max. thickness.

camber=4cm

pos. of camber=40 cm

max⁡ thickness=12 cm

NACA 23015,c=48 in., find the camber, position of camber and max. thickness.

camber=0.96 in

position of camber=7.2 in

max⁡ thickness=7.2in