This document discusses fluid dynamics and pressure. It defines density, pressure, and hydrostatic pressure. It provides examples of calculating hydrostatic pressure at different depths in fluids of varying densities. Formulas are given for calculating force, pressure, volume, and flow rate. Examples are worked through applying these formulas and concepts to problems involving submerged surfaces, fluids with different densities, and flow through pipes.

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2. 9
F
F F F
F F F F
F F F F F
9.1 F
F F F F F
F F (kg/m3)
=
- F F F
- F F F F F
3 3
4˚ C 1.0 x 10 kg/m
F 1
2 F F F 6.0 F F
d= 0.06
V= r3 = x 0.033
V = 1.13x10-4 m3
F = =
= 1.77 x 104 kg/m3 Ans
– F F www.schoolDD.com 1

3. 9.2
P F F ( )
F F F (Pa)
=
F
9.2.1 F
P0 g = gh
h Pg
P = P0 + gh
Pg h F
F gh
F P (Pg) (P0)
1.
2. F
– F F www.schoolDD.com 2

4. 3. F F
F F h
Pg = gh
4. F F F F F
F
h Pg = gh
5. F F
P = P0 + gh Pg Pg = gh Pg Pg = gh
= g = g = gh
P0
h h
F 2
F 5 F
F F ( F F F 1.02 x 103
kg/m3) , F 1.0 x105 Pa g = 9.8 m/s2)
P0 = 1x105
“ F F F ”
Pg h = 5.0
P
Pg = gh
= 1.02x103x9.8x5.0
Pg = 5.0 x 104 Pa Ans
F P = P0 + Pg
= 1.0x105 + 5.0x104
Pg = 1.5 x 105 Pa Ans
F 3
F 2 F F F 2.0 x 105 Pa F
P = P0 + Pg = P0 + gh
– F F www.schoolDD.com 3

5. F P = 2x105 F 2x105 = 1.0x105 + 1.02x103x9.8xh
h = 10.0 m Ans
9.3 F
F F = PA
F F
F
P0 Pg top = 0 P0
h =A h
Pg = gh
=A Pg bot = gh 0
F P = P0 + Pg P = P0 +
F = PA = (P0 + gh)A F = PA = (P0 + )A
- F F F
F (Po = 0) F F F F
F
F 4
F F F F F F F 2 F
F F F F ( = 1x103 kg/m3 , g = 9.8 m/s2)
Pg top = 0
2x2
h=2
Pg = gh
Pg bot = gh
– F F www.schoolDD.com 4

6. F F P = Pg = gh
= 1x103x9.8x2
P = 1.96x104 Pa
F = PA = 1.96x104x(2x2)
F = 7.84x104 N Ans
F P = =
=
P = 9.8x103 Pa
F = PA = 9.8x103x(2x2)
F = 3.92x104 N Ans
9.4
1. F
P0 P( F )
PB = PA
h Pg P = P0 + Pg
A B
P = P0 + gh
F
F F F F
2. F
( F)
PA = PB
P0 Pg h
P0 = gh
A B
– F F www.schoolDD.com 5

7. F 5
F (P0 =1.0 x 105 Pa , g = 9.8 m/s2 , =
3 3
13.6 x 10 kg/m )
P0
P=?
h= 0.1 Pg
A B
PA = PB
P0 + gh = P
35
1.0x10 + 13.6x10 x9.8x0.1 = P
P = 1.31x105 Pa Ans
F 6
F F F F F
F
P=?
h= 0.05 Pg
P0
F P0 = P + Pg
P = P0 – Pg = P0 - gh
= 1.0x105 - 1.0x103x9.8x0.05
P = 9.95x104 Pa Ans
F 7
F F F F
F F
P0
P
Pg h= 0.2
A B
– F F www.schoolDD.com 6

8. Pg PA = PB
Pg = gh
= 13.6x103x9.8x0.2
Pg = 2.66x104 Pa Ans
P F PA = PB
P F = Pg + P0
= 2.66x104 + 1x105
P F = 1.266x105 Pa Ans
F 8
F F F F F F 2 F F
F 103 kg/m3 F F 700 kg/m3
10 F F F
P0
P0
0.1
h= ?
A B
F F F
h PA = PB
Pg + P0 = Pg + P0
( gh) = ( gh)
700x9.8x0.1 = 103x9.8xh
h = 0.07 m
F F 0.10- 0.07 = 0.03 m Ans
– F F www.schoolDD.com 7

9. F 9
F x F F 1x103 kg/m3
P0
P0
0.1
A B
0.08
C D
x
PA = PB
PB = PC F
PC = PD
PA = PD
P0 + Pg = P0 + Pg x
( gh) = ( gh)x
3
1x10 x9.8x0.1 = x x9.8x0.08
x = 10/8 x103 = 1.25x103 kg/m3 Ans
9.5
– F F www.schoolDD.com 8

10. - F F F
F F
F
- F F F F F F F
F F F F
F
9.6
F F F F
F F
F
.a
(P=F/a F
)
F W
.A
.a
F = F
=
F 10
F F 10cm2 100 cm2 F
1000 kg F F F F F
– F F www.schoolDD.com 9

11. W
F
m = 1000 kg
.A
.a
=
=
F = 98 N Ans
F 11
F 10 F 100 N F F
( = 800 kg7m3)
W
F = 100 N m = 1000 kg
.A
.a x h
F
F x F = + gh
= + 800x9.8xh
h = 0.25 m Ans
– F F www.schoolDD.com 10

12. 9.7 F
FB F F F
F F F
V
V FB = m g= V g
mg FB FB = V g
mg FB FB ↑
- F FB = mg
- F mg > FB
T
mg FB a N + FB = mg
mg FB
FB = mg mg FB mg FB
FB = mg
mg - FB = ma N mgFB
T + FB = mg
F 12
F F 1 ( = 1x103 kg/m3)
. A F 50%
. B F
.
V = 0.5V
mg FB
FB = m g= V g
= (0.5V)g
= 1x103(0.5x1x1x1)x9.8
FB = 4900 N Ans
mg = FB = 4900 N
m = = = 500 kg
F = = 500 kg/m3
– F F www.schoolDD.com 11

13. .
V =V
mg FB
FB = m g = V g
= (V)g
= 1x103(1x1x1)x9.8
FB = 9800 N Ans
mg = FB = 9800 N
m = = = 1000 kg
F = = 1000 kg/m3
F 13
100 F
5 F F F F
1.2x103 kg/m3 F 103 kg/m3
F=5
mg FB
= 0
FB = F + mg
V g = F + mg
3
1x10 xVx9.8 = 5 + 0.1x10
V = = 6.12x10-4 m3
=
V = = = 0.83x10-4 m3
= 6.12x10-4 – 0.83x10-4 = 5.29x10-4 m3 Ans
F 14
F F 60 N F F 50 N F F
( = 1x103 kg/m3 , g = 10 m/s2)
– F F www.schoolDD.com 12

14. T T
mg mg FB
T = mg
60 = m(10)
m = 6 kg
T + FB = mg
T+ V g = mg
50 + 103xVx10 = 60
V = 10-3 m3
F = =
= 6x103 kg/m3 Ans
¬ F F F F F F
F
9.8
F F F F
F
F
F/2
T l
F T
F/2
L = 2l
F F
T
L = 2(2 r)
mg F
– F F www.schoolDD.com 13

15. ( ) F F F F
F (N/m)
=
- L
l L = 2l
F L = 2(2 r)
F L=2 r
-
F 15
F F 5 cm 15 cm 10 F 0.1 (N/m)
F F F F
T
mg F
= 0
T = F + mg
= L + mg
= 0.1(0.05+0.15)2 + 0.01x10
T = 0.104 N Ans
– F F www.schoolDD.com 14

16. 9.8.1 F
- F (cohesive force) F F
- (adhesive force) F
> F F >
- F F
F F
- F F F F F F
F F F
9.9
F F
FB F
F = 6 rv F
mg
( ) = (Ns/m2)
r = (m)
v = (m/s)
- F
- F F F F F
F F v
t
– F F www.schoolDD.com 15

17. -
- F F
F F
F 16
F 2 F
F F ( = 7.8x103 kg/m3, = 0.8x103 kg/m3, = 2.0 Pas, g
= 10 m/s2)
FB F
v
mg
v ( a = 0)
= ma = 0
F + FB = mg
F + V g = Vg
F = ( - )Vg
= (7.8-.08)x103x( (2x10-3)3)x10
F = 2.34x10-3 N Ans
F = 6 rv
2.34x10-3 = 6 (2.0)(2x10-3) v
v = 6.22x10-2 m/s Ans
9.10 F
(Av) F F
A2
v2
A1v1 = A2v2 F
A1 Av = F
v1 . F
– F F www.schoolDD.com 16

18. F 17
F F F F 20 cm F F
0.10 m/s
v = 0.1 m/s d = 0.2
= Av
= (0.2)2(0.1)
= 3.14x10-3 m3/s Ans
F 18
100 F F
F F F F 0.1 cm/s F F F
A1 A2
v1
v2
F A1v1 = A2v2
100x0.1x10-2 = 1xv2
v2 = 0.1 m/s = 10 cm/s Ans
9.10.1 F
FF F F F F F F
F F F
v2 A2
P + ½ v2 + gh = F P2
v1
h2
P1
h1
– F F www.schoolDD.com 17

19. P1 + ½ v12 + gh1 = P2 + ½ v22 + gh2 F
F h1 = h2
F P1 + ½ v12 = P2 + ½ v22
F h F F v P F
v F P
F 19
F F F F F F 8 cm2 F 1 F
1 m/s F F 4 cm2 F 9 F F F
3.0 x105 Pa
. F
. F
A2 = 4x10-4
v2 = ?
P2 = ?
A1 = 8x10-4
v1 = 1
h2 = 9
5
P1 = 3x10
h1 = 1
. v2 = ?
v2 F F A1v1 = A2v2
8x10-4x1 = 4x10-4xv2
v2 = 2 m/s Ans
. P2 = ?
P2 F F P1 + ½ v12 + gh1 = P2 + ½ v22 + gh2
3x105 + ½ x103x12 + 103x10x1 = P2 + ½ x103x22 + 103x10x9
P2 = 2.18x105 Pa Ans
– F F www.schoolDD.com 18

20. F 20
12 m F 6 m2 2.0 m F
F F F F F
P1 = P0
v1 = 0 A1 = 6
1
A2 << A1 F
FF F
h1 = 12
v2 = ? , P2 = P0 v1 = 0
2
h2 = 2
sx = ?
v2 F F P1 + ½ v12 + gh1 = P2 + ½ v22 + gh2
F P1 = P2 = P0 v1 = 0 F ½ v22 = g (h1 - h2)
v22 = 2 g (h1 - h2)
= 2x10 (12 – 2)
= 200
v2 = 14.14 m/s Ans
sx F F F sx = uxt = v2t
t sy = uyt + ½ ayt2
2 = 0 + ½ (10)t2
t2 = 0.4
t = 0.63 s
F sx = v2 t
= 14.14x0.63
sx = 8.94 m Ans
– F F www.schoolDD.com 19

21. F 21
F F 1050 N/ m2 F F
110 m/s F F F 1.0 kg/m3
P1
v1 = 120
v2 = ?
P2
F 1050 N/m2 F F
∆P = P2 – P1 = 1050
v2 F F P1 + ½ v12 + gh1 = P2 + ½ v22 + gh2
F h1 = h2 F ½ (v12 - v22 ) = (P2 – P1)
½ 1.0(1102 - v22 ) = 1050
v22 = 10000
v2 = 100 m/s Ans
– F F www.schoolDD.com 20