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Unformatted text preview: CEt 00
Midterm Examination
Fall 201 0
Friday, October 1 , 2010 Name 8 Z’ Student LD. This exam is open book and open notes. You will be given fifty (50) minutes to complete
two problems. Space is provided on each page for your soiution, the back of the pages
may also be used. Note that the first problem is worth 40 points and the 2”d is worth to;
allocate your time accordingiy. State clearly any assumptions you use in the solutions. Good Luck!
For reference: Atmospheric Pressure = patm = 100 kPa
Gravitationai Acceleration = g = 9.8 m/s2 Problem 1 (40 points): The set of tanks shown in the following diagram is designed to intermittently fill a water
bowl for a pet dog during an owner's absence. The system consists of two tanks,
connected by a small connecting pipe, and the water bowt. The first tank is maintained at
a constant depth, H1 2 0,15 m. The righthand—wall of the second tank is hinged at the
top, with a locking mechanism that can resist a moment of M0 = 265 Nm. When a '
counter—clockwise moment larger than M0 is applied around the hinge, the wall will open
momentarily and allow all water in tank 2 to drain out into the water bowl. Tanm _ Tank2 Water Bowl Additional measurements include: Depth of tank 1 (constant): H1 = 0.15 m
Surface area of tank 1: A1 = 0.0625 m2
Surface area of tank 2: A2 = 0.0625 m2 l
Crosssectionai area of connecting pipe: Apipe = .0001 m2
Height of the hinge above bottom oi tank 2: L = 0.25 m
Width of each tank into the page: W = 0.25 m Assuming that the second tank starts empty and that water is added to the first tank to
ensure H1 is constant: (a) Determine the depth of water in tank 2 when the gate opens. An exact soiution
to the equation is not necessary, an estimate to the nearest 5 cm is sufficient. (b) lnitlaiiy, tank 2 is completely empty. For this condition, determine the velocity of
flow going from tank 1 to tank 2. (0) Based on your answers to (a) and (b), you can define an estimate for how long it
will take for thewalt to open by assuming the veiocity calculated in (b) is constant
as tank 2 fiiis. In reality, wilt it take a longer or shorter time (than an estimate
based on constant velocity) for the wall to open? Explain your reasoning. NCMFQV" Lib; m . Mmmﬁvh‘s ‘CIL‘MK ﬁgp~£¢m 0 {rm/L 1* Cam—7% [TLF [A ’L‘. a we ‘1) v I Z ,
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WOL'jxs +0 ck CLQ ELL 0.53.12. Cy debt ail—.1 VIL {Rd/r! {bib {Mufkég 2:3) Problem 2 (1 0 points): A verticai pipe carrying flow Q = 0.5 mars downwards has an expansion from D1 = 0.5 m to D2 =1 m:
""" "Q" "um" 21 2 m, D; m Q = 0.5 m3/s Use Euler‘s equation to determine the pressure differenoe between points 1 and 2.
Could you have used the Bernoulli equation to do this calcuiation? Why or why not? “3%
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 Spring '09
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