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CE 330, Fall 07 Final Name ___________________________________ Problem 1 in a tank of water has a specific gravity of 0.7. (30 pts) The wooden solid body shown below (NOT specific weight!!!) in part (c). A figure is included for you use in drawing a The force F will only be considered FBD. (a) Determine the resultant vertical force exerted on thebody by the water. (b) Determine the resultant vertical force exerted on thetank bottom by the body. (c) Determine the minimum force F required to tip thebody assuming it will rotate about point o.
Part 1 V^ 70 (ft^3 )^ V (ft^3 )^ Bouyant 4368 F^ z (^) -3057.6 W (^) 0.666667 arm (^) Mome 873. (^23 28070 140) BouyantฮณV^ -8736 4368 -12230.4-3057.6 -5.66667-2.5 (^) -7425.6 52416 total^4 483^63 Bouyant^ 3931.2 3931.2^ -2751.84 -21097.4^ -9.25^ 34954.92 -10909. (b)(a)^ -17166 lb3931 lb (c) 3040 lb
F
o
L = 7โ
3-D nt^ 7โ
ZA = 350โ
A
Z B =?
120โ 75โ
25โ 180โ 160โ 130โ
100โ
For all pipes
ks = 0.0001โ
D = 6โ= 0.5โ
Kin. Vis = 10-5^ f
For all pipes
ks = 0.0001โ
D = 6โ= 0.5โ
Kin. Vis = 10-5^ f
For all pipes ks = 0.0001 ft D =1 inch ฮฝ = 10 -5^ ft 2 /sec
For all pipes
ks = 0.0001โ
D = 6โ= 0.5โ
Kin. Vis = 10-5^ f
For all pipes
ks = 0.0001โ
D = 6โ= 0.5โ
Kin. Vis = 10-5^ f
For all pipes ks = 0.0001 ft D =1 inch ฮฝ = 10 -5^ ft 2 /sec
Problem 2 system shown conveys water between (30 pts) The pipe
lakes A and B at the rate of 0.04 cfs.Determine the water surface elevation ofcoefficients are 0.5 and 1.0 and the Lake B if the entrance and exit loss loss coefficient for each of the 90degree bends is 0.9. Neglect local (or minor) losses in the parallel pipesystem. Also find the discharge in the 130-ft long pipe. Do not assume fullyrough turbulent flow.
Q cfs
h Q ft
Q z z ft
gD DfL K L K
R VD x f
V Q A fps
D
k
B B
total
s
203 ,. 50060 0.^0133
130
130 2 , 3 , 4 2 2
2 , 3 , (^42)
1 2 3 4 5
2 4
5 4
= โโโ^ +ฮฃ โโ โ= +ฮฃ
โ
(a) Problem 4 (30 pts) Joe Btfsplk is a character from theLil Abner cartoons. He is perpetually jinxed and alwayshas a rain cloud hovering over him. However, things may belooking up for him. He has invented a rain-poweredvehicle. The vehicle has a large funnel with an inletsection dimension of 24โ by 8โ and a circular 1-inch dia outletpipe that is directed 30 degrees to the horizontal as shown. When the rainfall rate is 40 inch/hr (quite high), his car is propelled at 10 fps. The raindrops fallvertically and have an absolute terminal velocity of 30 fps.
Free jet
D (^) outlet = 1โ
24โ by 8โInflow section 30 o 10 fps
Free jet
D (^) outlet = 1โ
24โ by 8โInflow section 30 o 10 fps
x
z
Free jet
D (^) outlet = 1โ
24โ by 8โInflow section 30 o 10 fps
Free jet
D (^) outlet = 1โ
24โ by 8โInflow section 30 o 10 fps
Free jet
D (^) outlet = 1โ
24โ by 8โInflow section 30 o 10 fps
Free jet
D (^) outlet = 1โ
24โ by 8โInflow section 30 o 10 fps
x
z
(a) Draw a picture of the tank in a co-ordinate system moving 10 fps in the positive x-direction. Compute and show the relative inflow and outflow velocities. (b) Determine the horizontal force imparted to the vehicle. (c) Determine the horsepower of the rain-powered vehicle assuming 100 percent (d) Determine the absolute velocity vector of the outgoing jet. Also, calculate theefficiency. (e)magnitude of the outgoing jet velocity.
( ) (^) ( )
1, 1, 1,^2 2 2 2 2 2,
40 / 1 / 1 / sec 24 8 0. 12 3600 / .178 / 0.00545 32.
rel abs rel o in out in out rel
a V V u k i i k V fps Q inch hr ft in hr x ft cf Q Q V V Q A cfs ft fps V
= โโ^ โโโโ^ โโ =
uuuuv uuuuv v v v v v
uuu v
s
( ) ( )( )
( )
, ,
2, 2,
o x o^ o x i i x x x abs rel
fps i k fps b F M V M V F lb c horsepower F u horsepower d V V u i k i i
u v v
uuuuv uuuuv v v v v (^) ( v ) 2, abs 24.
k fps V = fps
v
15-ft base width and 2 to 1 (hor:vert) side slopes Problem 5^ (40 pts) A trapezoidal channel with a flows uniformly at a depth of 12 feet.rectangular culvert. Determine the following. It flows into a
10โ y (^2)
flow y 10โ 1 y (^2)
flow y 1
(a) The discharge if the Froude number of the uniform flow in the trapezoidal channel is 0.2. (b) The Manningโs n-value of the trapezoidal channel for a channel bed slope So = 0.0007. (c) The minimum width of the RCB (reinforced box culvert) required to pass the flow withoutcreating a choke if the entrance loss coefficient is 0.7. Assume inlet control (thus y critical).^2 is (d) Determine ydetermined in Step (c). 1 and y 2 if a 12-ft wide RCB culvert is installed rather than the one (e) If two 12-ft diameter circular culverts are installed instead of the RCB, it is known thateach culvert is half-full at the critical inlet section. Determine the depth of flow at Section 1 and classify the type of GVF profile as M 1 , M 2 or M 3.
( (^ ) )
2 2 3 3 2 2 3
(^2 )
5 / 3 2 / 3
1 2 1
r
o r o ent c
a F Q T Q gA
gA T
Q
Q cfs
b Manning s
n
n
c E ft F
E E K y z z
= = โโ^ โโโ =
2 3 2
c c c c min
y y
y ft
q gy cfs ft
b Q ft
q
(^22) 2 1/ 3 2 2 1 1 (^22)
3
1
1 2 1
c
SE
c ent c c SE
d q Q cfs
b
y y q ft
g
E ft
y ft
e A ft T ft
Check Q g NOT ok
E y k A
T
E ft M curve y ft
ฯ
= = โโ^ โโ =
= โโ^ โโ= =
Problem 7 rectangular channel as shown. There is a (40 pts) Water flows in the smooth transition from Section 1 to Section 2. (a) Determine y 2 and the change in water
(b) For bsurface elevation if^ ฮz = 1.5 ft and b^2 = 13 ft. produces a 1 ft drop in the water surface^2 = 13 ft, find the value of^ ฮz that (c) Determine the maximum allowable valueelevation from 1 to 2. ofbe avoided. ฮz if b 2 equals 11 feet and a choke is to
( )
( )
(^1 12 ) 1 1 1 (^1 1 22 2 ) (^2 2 2 ) 2 22 2 2 2 2 2
a Q V A x cfs E y V ft g E z E z E f y Q y g y y y (^) y y ft y z ft ws ft b q Q b cfs ft
b 1 = 10โ b 2
y 1 = 12โ y^2 ฮz Plan View
Elevation View V 1 = 4 fps
t
( )
( ) ( )
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2
22 2 2 (^2 2) 1/ 3 2 22 2 1 2 2 1 2
11 4.12 6.88 6.88 \
c c c
y z z y y q z y z gy y y (^) y y
y y^ ft z ft z c q Q b cfs ft y y q g ft E E y ft E E z z E
ft
max 1 2 12.25^ 5.84^ 6.
z z E E ft
