how do you figure out this problem? ENGR 391/ HW 3 Q5) Consider a fluid flow bet

Question

how do you figure out this problem?

ENGR 391/ HW 3 Q5) Consider a fluid flow between two fixed parallel walls that are H 5 cm apart. The channel has a width (into the plane of your semen) of m. The fluid is water, with density 1000 kg m3, and viscosiry 0.92 N. m. The velocity distribution of the flow is given by the equation L Mass conservation a. Use the given velocity profile to determine the mass flow rate through the channel. (hint: b. Using this value of mass flow rate found in part a cakulale the average channel velocity v Use the givsa velosity file to determine the maximum fie mid-channen velocity U.un. d, the mid-channel height) and geometry? This value should not have been what is the for this flow assumed in your working in parts a-e.) IL Visrous shear e, calculate the magnitude of the shear stress at he wall s (hint: dinerentiation moed di

Explanation / Answer

given velocity profile u(y) = 110(0.05*y - y^2)
a) assume a incremental height of water of thickness dy, at height y
assume channel depth of d
area of this water element = d*dy
incremental flow rate, dF = rho*v(y)*d*dy
dF = rho*110*(0.05y - y^2)*d*dy
integrating from y = 0 to y = H
F = rho*110*d*(0.05H^2/2 - H^3/3)
H = 0.05 m
d = 1 m
F = 2.2916 kg m/s
b) Average channel velocity = v
then v*d*H*rho = F = 2.2916
v = 2.2916/0.05*1*1000 = 0.0458 m/s
c) u(y) max is at y = H/2
u(H/2) = 110(0.05*H/2 - H^2/4)
now H = 0.05 cm
u(H/2) = 0.06875m/s
d) V/Umax = 0.66618

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