Problem # 4 in the picture Steam enters a nozzle with a low velocity at 300 degr

Question

Problem # 4 in the picture

Steam enters a nozzle with a low velocity at 300 degree F and 30 PSI, and leaves as saturated vapor at 10 PSI There is heat loss from the nozzle in the amount of 25 BTU/lbm Determine the exit velocity of the steam (ft/s) and the mass flow rate (Ibm/s) of the steam at the nozzle entrance if the nozzle exit area is 0.01 ft2. A spherical balloon filled with Helium is initially at 300 K and 100 kPa with a diameter of 5 cm The balloon is inflated until it contains 4 times its initial mass During the inflating heat is being transferred to the balloon such that the final temperature of the Helium is 450 K Due to the e elasticity of the balloon the pressure remains proportional to the diameter squared D2)at a times Determine the work (kJ) and heat transfer (kJ) associated with this process. Note: for Helium Extra credit Enrich Weiss died October 31, 1926 at the age of 52 Detroit, he was famously known by this name

Explanation / Answer

P1 = 100000 = k*0.05^2

k = 4*10^7

P2 = 4*10^7*(4^(1/3)*0.05)^2 = 251.98kPa

P= k*d^2

P=k*(6V/3.142)^(1/3)=4*10^7*1.24*v^(1/3)= 4.96*10^7*v^(1/3)

w = int. PdV = 3.72*10^7*(V2^(4/3)- V1^(4/3))

V2 = 3.142*(4^(1/3)*0.05)^3/6 = 0.0002618333

V1 = 3.142*(0.05)^3/6 = 0.00006545833

W = 3.72*10^7*(0.00001675071-0.00000263807) = 525J work done

Q = U + w = nCpdT + w

n = 10^5*0.00006545833/(8.314*300) = 0.00262

Q = 0.00262*2.5*8.314*150 + 525 = 533.168 J heat

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