Question

One day Daniel Bernoulli was sitting in a Starbucks sipping on a Venti Mocha Frappuccino. He pondered some of the many applications of his newly developed principle. Grab a Starbucks of your own, and help him to answer the following questions. Assume air wehs 0.081 lb/ft3 NOTES IMAGES DISCUSS UNITS STATS HELP Part Description Answer Chk History In a hurricane, roofs of structures are really lifted off, and not blown off, due to the decreased pressure as the wind blows over the roof. Determine the required wind speed to lift a roof that welghs 17 psf Assume the roof is not tied down (include units with answer) 18.33 pts. 110% 2%try puraty Hints: 1.0 # tries: 0 Show Details Fomat Cheok Determine the minimum required take-orr speed of a 29000 pound UScalrways jet with a wing area of 1420 ft2, Use a lift coefficient of K-0.12 (include units with answer) 18.33 pts, 1 10% 2 try peraty Hints: 1.0 B. # tnes : O Snow Details Format Ghook " Daniel's good friend Giovanni Venturi joined him for another round of fraps. They were discussing ways to determine the velocity of water in a pipe. If the pressure drops 390 kPa as water flowing in a 50 cm diameter pipe is forced to flow through a 20 cm diameter portion, what is the velocity of the water in the 50 cm section of pipe? (include units with answer) 18.33 pts,110% C. # tries: ( Snow Details 2% try par.tv Hints: 10

Answer 1

A) Here, we are using the following formula for v to calculate speed v

Here, we are using the following formula for v to calculate speed v v = squareroot 2P/p...(a) P is the pressure, rho is the air density and putting all the parameters in SI units v = squareroot 2 times 813.98/1.297 = 35.43 m/s Here, two forces are acting one is the lifting force F which can be given as F_2 = 1/2 pv^2 KA...(1) rho is the air density, v is the speed that needs to be determined and K, A are lifting coefficient and area, respectively. The second force f2 is given as F_2 = mg...(2) Lifting will take place only if two forces balancing each other 1/2 pv^2 KA = mg Solving for v, we get v = squareroot 2mg/pKA Here, we are putting all the values in SI system v = squareroot 2 times 1315.4 times 9.8/1.297 times 0.12 times 131.9 = 17.35 m/s Here, we need to use the Bernoulli's principle and equations which can be given as follows

P is the pressure, rho is the air density and putting all the parameters in SI units

B) Here, two forces are acting one is the lifting force F which can be given as

rho is the air density, v is the speed that needs to be determined and K, A are lifting coefficient and area, respectively. The second force f2 is given as

Lifting will take place only if two forces balancing each other

Solving for v, we get

Here, we are putting all the values in SI system

(c) Here, we need to use the Bernoulli;s principle and equations which can be given as follows

We have used the subscripts 1 for 50 cm diameter pipe and subscript 2 for 20 cm diameter pipe. A, v, P, g, h represent area, speed, Pressure, acceleration due to gravity and height, respectively... We have assumed that the height h remains the same. The cross sectional area is circular and is equal to pi r² with r is the radius. Firstly, we solve the first equation to find v2 in terms of v1 as we are looking to find v1/

Pressure drop P2-P1=390KPa so using Eq. (2c) along with Eq. (3c) to find v1