Elb-
72 U CHAPTERS
3.53
3.54
I (a) F = mg = (62.4)[14 + (%)/2][(ig)(%)] = 25 740 lb. Let T = force parallel to gate required
to open it. )3 F, = 0; T 1000 (0. 5)(25 740) = 0, T = 13 870 lb. (b) See Fig. 3411;. F =
(62.4)[14 + i2(1/\/)/2][(%)(%)] = 23 584

FLUID STATICS U 43
Mercury (s.g. = 13.6) Fig 2-44
2.62 Vessels A and B in Fig. 245 contain water under pressures of 40.0 psi and 20.0 psi, respectively. What is the
' deection of the mercury in the differential gage?
I (40.0)(144) + (62.4)(x + h) [(13.6

FLUID STATICS U 41
Mercury
(5-: = 13.6) Fig. 2.40
2.58 A dierential manometer is attached to two tanks, as shown in Fig. 2-41. Calculate the pressure difference
between chambers A and B.
l pA + [(0.89)(9.79)](1.1) + [(13.6)(9.79)](0.3) [(1.59)(9.79)](0.

min
OD
9 (ohm)
w (omega)
P
P
Pa
(phi)
1: (pi)
H (pi)
P, .
p3 .
p81
is .(PSi)
pSla
vas
p
pg
pW
q
Q
Q"
Q/w
qt
r
R
R!
rad
RC
Rh
0 (the)
n
0
rpm
Rll
S
s
Sc
s.g.
Sig.
s.g.F
ABBREVIATIONS AND SYMBOLS 0 ix
milliliter (103 L)
minute
millimeter (103 meter)
megane

0.00001667 m3/s = 1 L/min
0.002228 ft3/s = 1 gal/ min
0.0145 lb/in2 = 1 mbar
0.3048 m = 1 ft
2.54 cm = 1 in
3.281 ft = 1 m
4 qt = 1 gal
4.184 U = 1 kcal
4.448 N = 1 lb
6.894 kN/m2 = 11b/in2
7.48 gal = 1 ft3
12 in = 1 ft
14.59 kg = 1 slug
25.4 mm = 1 in
60

CONTENTS
To the Student v
List of Abbreviations vii
List of Conversion Factors xi
Chapter 1 PROPERTIES OF FLUIDS 1
Chapter 2 FLUID STATICS 25
Chapter 3 FORCES ON SUBMERGED PLANE AREAS 53
Chapter 4 DAMS _ TI
Chapter 5 FORCES ON SUBMERGED CURVED AREAS 85

50 U CHAPTER 2
2.83
2.84
2.85
2.86
2.87
2.88
2.89
2.90
Find the force of oil on the top surface CD of Fig. 2-62 if the liquid level in the open pipe is reduced by 1.3 m.
' pa, [(0.8)(62.4)][4 - (1.3)(3.281)] = 0 pa, = 13.24 lb/ft2 (i.e., a downward pressu

2.80
2.81
2.82
FLUID STATICS U 49
In Fig. 2-60a the inclined manometer measures the excess pressure at A over that at B. The reservoir diameter
is 2.5 in and that of the inclined tube is % in. For 0 = 32 and gage uid with s.g. = 0.832, calibrate the scale

74
3.57
3.58
0 CHAPTER 3
Determine the force acting on one side of vertical surface OACO in Fig. 3-46 and the location of the center of
pressure, if y= 8. 4 kN/ms. The curved edge' 15 an arc of the parabola y= x2/ 8
I F = f yy dA = J, 1(8.4)(y)(2x dy) %

FORCES ON SUBMERGED PLANE AREAS U 69
3.44 Circular gate ABC in Fig. 3-35 is 4 min diameter and is hinged at B. Compute the force P just sufcient to keep
the gate from opening when h is 8 m.
I F = yhch = (9.79)(8)[(4)2/4] = 984.2 kN 1, = er4/64 = n:(4)4/64

FORCES ON SUBMERGED PLANE AREAS U 67
.1 (View
I
Water ._.
ikIJL
B keft ~lC
\ mg. 330(4) Fig- 3-300)
Spherical
Fig. 3-31
3.40 The triangular trough in Fig. 332 is hinged at A and held together by cable BC at the top. If cable spacing is
1 [11 into th

FORCES ON SUBMERGED PLANE AREAS U 75
Determine y in Fig. 3-48 so that the ashboards will tumble only when the water reaches their top.
I The ashboards will tumble when y is at the center of pressure. Hence, y = g, or 1.333 m.
I Fig.3-48
: 3.60 Determine

66 0 CHAPTER 3
25cm
B
k120cm-cfw_c Fig. 3.23
3.37 Water in a tank is pressurized to 85 cmHg (Fig. 3-29). Determine the hydrostatic force per meter width on panel
AB.
I On panel AB, pcg = [(13.6)(9.79)](0.85) + (9.79)(4 + %) = 167.0 kPa, FAB = (167.0)[

A1 -. :3?-
36 0 CHAPTER 2
2.45
2.46
2.47
p
l.
l.
m
I
Water
3.5 ft
4" 35ft
7 l
m" Fig. 2-27(a)
In Fig. 2-28a, A contains water, and the manometer uid has density 2900 kg/m3. When the left meniscus is at
zero on the scale, p, = 100 mm of water. Find the rea

68 U CHAPTER 3
3.41 In Fig. 3-33, gate AB is 4 ft wide and opens to let fresh water out when the ocean tide is falling. The hinge at A
is 3 ft above the fresh-water surface. At what ocean depth h will the gate open? Neglect the gates weight.
I F = yhch E

1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
PROPERTIES OF FLUIDS U 3
If the tank of Prob. 1.17 holds 30.5 kg of salad oil, what is the density of the oil?
' Vm = 2094 in3 (from Prob. 1.17)
= %9%(0.3048)3 = 0.03431 m3
p = m/V = 30.5/0.03431 = 889 kg/m3
Un

Abbreviations and Symbols)
a acceleration or area
A area
abs absolute
0: (alpha) angle between absolute velocity of uid in hydraulic machine and linear velocity of a point on a
rotating body or coefcient of thermal expansion or dimensionless ratio of simi

4 U CHAPTER1
1.27
1.28
1.29
1.30
1.31
1.32
If K = 2.2 GPa is the bulk modulus of elasticity for water, what pressure is required to reduce a volume by 0.6
percent?
l K Ji 22~12_0 p2=0.0132GPa or 13.2MPa
_AV/V ' " 0.006
Find the change in volume of 1.000

x 0 WWW AND SYMBOLS
a (sigma) pump cavitation parameter or stress or surface tension L
l ,
a cavitation index ,3 3
2 (sigma) summation
S specific gravity of owing uid
So specic gravity of manometerguid
: ' thickness or time
T surface width or temperatu

1.1
1.2
1.3
1.4
1.5
1.6
1.7
CHAPTER 1
Properties of Fluids
Note: For many problems in this chapter, values of various physical properties of uids are obtained from
Tables A-1 through A-8 in the Appendix.
A reservoir of glycerin (glyc) has a mass of 1200 k

110 0 CHAPTER 6
6.9
6.10
6.11
6.12
6.13
6.14
A hollow cube 1.0 m on each side weighs 2.4 kN. The cube is tied to a solid concrete block weighing 10.0 kN.
Will these two objects tied together oat or sink in water? The specic gravity of the concrete is 2.40

CHAPTER 3
Forces on Submerged Plane Areas
. 3.1 If a triangle of height d and base b is vertical and submerged in liquid with its vertex at the liquid surface (see
Fig. 3-1), derive an expression for the depth to its center of pressure.
1.5 34+ bd3/36 _3

i 1
106 0 CHAPTER 5
5.50
5.51
5.52
5.53
5.54
A 48-in-diametcr steel pipe, % in thick, carries oil of s. g. = 0.822 under a head of 400 ft of oil. Compute the
(a) stress in the steel and (b) thickness of steel required to carry a pressure of 250 psi with a

FLUID STATICS [7 47
2.73 For Fig. 2-53, if uid 1 is water and uid 2 is mercury, and 2, = 0 and 21 = 11 cm, what is level 22 at which
pA :17 arm?
I 0 + (9.79)[o (11)]/100 [(13.6)(9.79)][zz (1i)]/100 = 0 22 = 10. 19 cm
09" potm
\
/
2 Fig. 2-53
2.74 The

54 U CHAPTER 3
rba
cl
_L Fig. 3-3
3.4 A circular area of diameter d is vertical and submerged in a liquid. Its upper edge is coincident with the liquid
surface (see Fig. 3-4). Derive an expression for the depth to its center of pressure.
1., _d inf/64 d

100 [7 CHAPTER 5
5.30 Gate AB in Fig. 5-30a is 7 m wide into the paper. Compute the force F required to prevent rotation about the
hinge at B. Neglect atmospheric pressure.
I F" = yEA = 9.79[(9.6 + 0)/2][(9.6)(7)] = 3158 kN. F acts at 355, or 3.200 m abov