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Unformatted text preview: ME332 Final Exam Lecture section 2 (MWF: 3:00 — 3:50) April 30, 2003 Name: Student No. Instructions
1. There are four problems. Allocate your time and eﬂort to maximize your points.
2. Layout your work clearly and show your reasoning. 3. This is an open—book (Text Book) examination. One 8%X11 paper allowed. Problem 1. (25%) Determine the force P needed to hold a rectangular 4—m—wide (into the paper) gate in the position
shown in Figure 1. The weight of the gate is 20000 N. Egg: tee/vet lg 3352 gig/é: iwiéwig ‘ . "~+~ $379??? x m  we,“ we ~a
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I ” rye Problem 2. (25%) Water at 20” C ﬂows steadily through the box (see Figure 3). The velocity at the inlet station (1)
is 2 m/s. Calculate (a) the horizontal and (b) vertical forces required to hold the box stationary
against the ﬂow momentum. Sketch both the horizontal and the vertical forces with directions. #th it’iflgvfagg é§ m yle 2
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gar.» gaggle: Wrgg wfétﬁiitei grimy: f2 g 23%é/e‘égwg § Problem 3. (25%) An incompressible, laminar, Viscous ﬂuid is placed between inﬁnite, inclined, parallel plates as
is shown in Figure 3. The two plates move in opposite directions with constant velocities, U1 and U 2 , as shown. The pressure gradient in the x direction is zero. (a) Simplify the Navier—Stokes equations to derive a differential equation for the velocity
distribution between the plates. (b) Specify the boundary conditions for the differential equation. (c) Solve the differential equation for the velocity distribution. (b) Calculate the average velocity V of the ﬂuid layer between the two plates. avg Problem 4. (25%) Oil is transported steadily with a ﬂow rate of 0.1m3 /s by commercial—steel pipeline from a reﬁnery to a seaport terminal that is 800 kilometers away. The diameter of the pipe is 0.35m and
the oil has a speciﬁc gravity of 0.8 and a Viscosity of 0.002 kg/ m ' s. If the absolute pressure at
the reﬁnery is 1000 kPa and the absolute pressure inside the pipeline must not drop below 60
kPa, at what distance from the reﬁnery must the ﬁrst pump be placed? If this pump raises the
pipeline pressure back to 1000 kPa, how many such pumps are required to pump the oil to the
seaport terminal? (neglecting the elevation changes between the reﬁnery and the seaport
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 Spring '10
 GOLDSTEIN
 Fluid Dynamics, Velocity

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