Subject: Fluid Mechanics MEC 205
Year: 2025/2026
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Sheet (3)
1- For steady, incompressible flow, verify whether the following values of u and v are possible:
(i) u = 4xy + y2 , v = 6xy + 3x
(ii) u = 2x2 + y2 , v = - 4xy
(iii) u = - x/(x2 + y2) , v = - y/(x2 + y2)
2- Determine which of the velocity component sets given below satisfy the equation of
continuity:
(a) u = cx
v = -cy
(b) u = - cx/y
v = c ln xy
(c) u = A sin xy
v = - A sin xy
(d) u = x + y
v = x –y
(e) u = 2x2 + zy
v = - 2xy + 3y3 + 3zy
w = - 3/2 z2- 2 xy – 6yz
3- A velocity field is given by u = A cosθ, v = A sinθ, and w = 0, where A and θ are constants.
Find an expression for the streamlines of this flow. If A=2 and θ=45 degrees, draw the
streamline passing through point (0,1).
4- Water flows through a pipe AB of diameter d1 = 50 mm which is in sense with a pipe BC of
diameter d2 = 5 mm in which the mean velocity V2 = 2 m/s. At C the pipe forks and one
branch CD is of diameter d3 such that the mean velocity V3 is 1.5 m/s. The other branch CE
is of diameter d4 = 30 mm and conditions are such that the discharge Q2 from BC divides so
that Q4 = 1/2 Q3. Calculate the values of Q1, V1, Q2, Q3, d3, Q4 and V4
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5- Gasoline enters section 1 at 0.5 m3/s. It leaves section 2 at an average velocity of 12 m/s. What
is the average velocity at section 3? Is it in or out?
.
6- The natural gas (methane) and crude oil mixture enters the separator at A at 6 ft3/s and passes
through the mist extractor at B. Crude oil flows out at 800 gal/min through the pipe at C, and
natural gas leaves the 2-in-diameter pipe at D at VD = 300 ft/s. Determine the specific weight
of the mixture that enters the separator at A. The process takes place at a constant temperature
of 68°F.
Take ρo = 1.71 slug/ft3, ρme = 1.29(10-3) slug/ft3. Note 1 ft3 = 7.48 gal
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