(20%) Problem 5: Gasoline is piped underground from refineries to major users. T
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Question
(20%) Problem 5: Gasoline is piped underground from refineries to major users. The volume flow rate is 5.2 × 10-2 m, s, the viscosity of gasoline is 1.00 x 103 N/m2)s, and its density is 680 kg/m3 Randomized Variables Q-5.2 x 10-2 m3/s - 50% Part (a) What is the minimum diameter, in meters, the pipe can have for the flow to be laminar? Take 2000 for the maximum value of the Reynold's number for laminar flow 50% Part (b) What pressure difference in pascals, must be maintained along a pipe of length 0.5 km to maintain this flow rate? Grade Summary Deductions Potential 0% 100% sin0 7 8 9 cosO cotan0asin acos0 atan0 acotan sinhO cosh0 tanh cotanh0 O Degrees Radians tan Submissions Attempts remaining: Z (30% per attempt) detailed view *12 3 END Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback.Explanation / Answer
Given,
V = 5.2 x 10^-2 m^3 ; viscosity = eta = 1.00 x 10^-3 N/m^2 ; rho = 680 kg/m^3
We know that
Nr = 2 rho v r/eta = 2000
v = Q/A = Q/pi r^2
2 rho Q/pi r^2 eta = 2000
r = rho Q/pi eta 1000
r = 680 x 5.2 x 10^-2/3.14 x 1 x 10^-3 x 1000 = 11.26
d = 2 x 11.26 = 22.52 m
Hence, d = 22.52 m
b)L = 9.5 km
Q = delta-P pi r^4/8 eta l
delta P = 8 eta l Q/pi r^4
Q = 8 x 1 x 10^-3 x 9500 x 5.2 x 10^-2/[3.14(22.52)^4] = 4.89 x 10^-6 N/m^2
Hence, P = 4.89 x 10^-6 N/m^2 = 4.83 x 10^-11 atm
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