Math Field Day 2012 Short Course Event
Names _____CALCS KEY___________________
48 points total
School ________________________________
Scores
part one: number correct______ x 4 = ______ minus number wrong ______ = ______(A)
Part one Instructions: Work in teams of two. You should use the formulas, constants, and conversion factors
provided and your notes. Record your answers by circling the letter to the right. Each correct answer worth 4
points; one point will be deducted for each wrong answer. (Maximum score on part 1 is 24 points.)
In problems 1 through 6 you are to choose the closest answer.
1.
Q  AV
Continuity:
  2 
ft
gal
s
 Q    3  / 4 ft 2  10  60
 7.48 3  220.3 gpm
s
min
ft
  12  
(a) 22
2.
3.
(b) 36
(c) 220
(d ) 361
a
b c d
e
a
b c d
e
a
b
c
a
b
c d  e
a
b c d
(e) 440
1 min
1 ft 3

 1.114cfs
60 sec 7.48 gal
A V
Q
1.114
 V6  12 12  
 5.67 ft sec
A6
A6  4 ( 12) 2
(a) 1.42
(b) 14.2
(c) 5.67
(d ) 9.20
(e) 56.7
500 gpm 
Continuity:
Unit Conversion:
28
mg
gal
1 ft 3
1day
 10 6


 43.33cfs
day
mg 7.48 gal 24  3600 sec
(a) 1.55cfs
4.
Circle the letter of the correct
answer
(b) 15.5cfs
(c) 23.7cfs
(d ) 31.5cfs
d
e
(e) 43.4cfs
Darcy-Weisbach:
2
12
2
2
 L  V 
 L  Q A 
 1000  ( d 2 4 ) 
  f  
hL  f  
 .0155
4

 d  2 g 
 d  2g
 d  2(32.2) 
 d 1.696 ft  d  20.3 in
(b) 15 in
(c) 18 in
(d ) 21in
(e) 24 in
Solve for d or use solver
(a) 12 in
5.
V2
Velocity head and static head: hs 
2g
 V  2 ghs
 V  2(32.2)10  25.38 ft
(a) 12.2
(b) 17.9
(c) 25.4
3
6.
(a) 1.
(d ) 29.2
V
(e) 35.8
gal 1 min
1 ft 3


min 60 sec 7.48 gal
Q

A
 4  .5 122 ft 2
(b) 5.
(c) 10.
(d ) 20.
Unit Conversion:
ft
sec
(e) 50.
 4.9
a b c
d
(over)
Math Field Day 2012
e
sec
“Respect for the rights of others is peace.” BJ
http://www.cuyamaca.edu/bfurry

Furry 3 /10/12
e
Math Field Day 2012 Short Course Event
Names _____CALCS KEY___________________
48 points total
School ________________________________
part two: number correct______ x 4 = _______ minus number wrong ______ = _______(B)
Part two Instructions: Work in teams of two. You should use the formulas, constants, and conversion factors
provided and your notes. Record your answers by circling the letter to the right. Each correct answer worth 4
points; one point will be deducted for each wrong answer. (Maximum score on part 2 is 24 points.)
Circle the letter of the correct
In problems 7 through 12 you are to choose the closest answer.
answer
7.
Energy equation: (Static heads are equal and so cancel; hL  0 .)


v1  Q A1  125.6 /  2 / 4  39.98 ft s
2
2
1
and
v 2  4.44 ft s
2
2
p1 v
p
v

 z1  2 
 z 2  hL 
w 2g
w 2g
a
c d  e
b
 18  39.98 2 (2  32.2)  0  p 2 w  4.44 2 (2  32.2)  0  0
 p 2 w  42.5 ft
(a) 3.5 (b) 15.0 (c) 28.5 (d ) 42.5 (e) 57.5
Hydraulic Jump:
8.
9.
q 2 g  12 y1 y 2 ( y1  y 2 )  192 / 16 / 32.2  2.10 y1 ( y1  4.20)
 y1  0.455
(a) 0.213 (b) 0.455 (c) 1.10 (d ) 1.39 (e) 1.51
a b c
2
d
e
a
b c d
e
a
b
a
b c
Loss of head in Hydraulic Jump = E1  E 2
A1  16 0.455  7.29 ft 2 , V1  192 / 7.29  26.3 ft / sec
A2  16(4.20)  67.2 ft 2 ,
V2  192 / 67.2  2.86 ft / sec
E1  (26.3) 2 2 g  0.455  11.18 ft ,
E 2  (2.86) 2 / 2 g  4.20  4.33 ft
11.18  4.33  6.85 ft
10.
Manning formula:
6.00 
11.
(a) 1.19 (b) 3.49 (c) 6.85 (d ) 8.22 (e) 11.18
1.486 2 3 12
QA
R S
n
  1.486  1 
2
3

  S
2  .013  2 
1
solve for
2
S or use solver
c
d
e
d
e
 S  .00281
(a) .0004
(b) .0008
(c) .0009
(d ) .0012
(e) .0028
1.486 2 3 12
Manning formula:
QA
R S
n
2
3
1
 1.486  6w 
500  6w

 .0004 2 use solver  w  13.1 ft
 .010  w  12 
(a) 6.2 ft
(b) 10.1 ft
(c) 13.1 ft
(d ) 15.6 ft
(e) 19.2 ft
A circle  (sec tor  triangle )

12. Hydraulic Radius: R 
wp
Arc
 d2
A
R

wp
(a) 0.298d
1
 2

 ( d  2 cos (.8)   12  .6d  .4d )
4  4
2
 .298d
 d  2 cos 1 (.8)  d / 2
(b) 0.304d (c) 0.632d
(d ) 0.98d
(e) 1.50d
Math Field Day 2012
“Respect for the rights of others is peace.” BJ
http://www.cuyamaca.edu/bfurry
a b

c
Furry 3 /10/12
d
e