moral questions. These issues include:#### 2.1 **Patient Autonomy and Informed
Consent**One of the fundamental ethical principles in healthcare is respect for patient
autonomy—the right of patients to make decisions about their own bodies and medical
treatments. This principle is enshrined in the legal concept of informed consent.
Informed consent requires healthcare providers to disclose all relevant information
about the risks, benefits, and alternatives to a medical treatment or procedure,
allowing patients to make informed decisions.However, challenges arise when patients
are not fully capable of making informed decisions (e.g., due to age, mental illness, or
language barriers). In such cases, ethical dilemmas can arise regarding whether a third
party (e.g., a parent or guardian) should make the
Chapter 1
1.1 V1 T1p2
Since pV = mRT, =
V1 T2p1
π288.15 1.1
∴ V1 = (20 m)3 = 56.2 m3
6 233.15 101.3
1.2 p 1.4 × 105 N · m−2 −3
ρ= = = 1.51 kg · m
RT 287 J · kg−1 · K−1 × 323.15 K
∂p p − p0
1.3 K=ρ Assume K constant. Then ln(ρ/ρ0) =
∂ρ K
p − p0 81.7 × 106
∴ ρ = ρ0 exp = 1025 kg · m−3 exp
2.34 × 109
= 1061 kg · m−3
1.4 µ 2 10−5 N s m−2 3
ρ= = = 1.333 kg · m−
ν 15 × 10−6 m2 · s−1
p 1.013 × 105 N · m−2 259.2 J kg−1 K−1
R
= = = · ·
1.333 kg · m−3 × 293.15 K
ρT
8310
∴M= = 32.06
259.2
1.5 µ = νρ = 400 × 10−6 m2 · s−1 × 850 kg · m−3 = 0.34 Pa · s
0.12 m · s−1
Velocity gradient −1
= = 1200 s
0.1 × 10−3 m
Area = π 0.2 × 1.2 m2 = 0.754 m2
Force = 0.754 m2 × 0.34 Pa · s × 1200 s−1 = 307.6 N
, 2 Solutions manual
1.6 ∂u ∂u
Total force on plate = Area × µ +
∂y side A ∂y side B
0.15 m s−1
+ 0.15 m · s
2 −1
= (0.25 m) × 0.7 Pa · s 0.006 m 0.019 m
= 1.439 N
1.7 For annulus, radius r, width δr
Velocity ωr
Force Area µ = 2πrδrµ
= × ×
Clearancec
µω
∴ Torque = Force × r = 2πr3δr
c
∫ R
µω π R4µω
Total torque = 2π r3 dr =
0 c 2c
−1
π( 0.1 m) 0.14 Pa s × 2π × 7 rad s
4
= = 7.44 N · m
2 × 0.00013 m
1.8
2γ 2 × 0.073 N · m−1
p= = = 36.5 Pa
d 0.004 m
1.9 h 4γ cos θ 4 × 0.073 N · m−1 × 1
= =
ρgd 1000 kg · m−3 × 9.81 N · kg−1 × 0.005 m
= 0.00595 m = 5.95 mm
1.10 4 × 0.377 N · m−1 × cos 140◦
h
=
(13.56 − 1)1000 kg · m−3 × 9.81 N · kg−1 × 0.006 m
= −1.563 mm
1.11 Re udρ 4Qρ 4 × 0.0025 m3 · s−1 × 900 kg · m−3 1508
= = =
µ πdµ =
π 0.05 m × 0.038 N · s · m−2
2000µ2000 × 0.038 N · s · m−2
u= = 1.689 m · s−1
dρ −3
=
0.05 m × 900 kg · m
1.12 Re 4Qρ 4 × 0.01 m3 · s−1 430 Laminar
= = = ∴
πdµ π 0.08 m × 370 × 10−6 m2 · s−1
Consent**One of the fundamental ethical principles in healthcare is respect for patient
autonomy—the right of patients to make decisions about their own bodies and medical
treatments. This principle is enshrined in the legal concept of informed consent.
Informed consent requires healthcare providers to disclose all relevant information
about the risks, benefits, and alternatives to a medical treatment or procedure,
allowing patients to make informed decisions.However, challenges arise when patients
are not fully capable of making informed decisions (e.g., due to age, mental illness, or
language barriers). In such cases, ethical dilemmas can arise regarding whether a third
party (e.g., a parent or guardian) should make the
Chapter 1
1.1 V1 T1p2
Since pV = mRT, =
V1 T2p1
π288.15 1.1
∴ V1 = (20 m)3 = 56.2 m3
6 233.15 101.3
1.2 p 1.4 × 105 N · m−2 −3
ρ= = = 1.51 kg · m
RT 287 J · kg−1 · K−1 × 323.15 K
∂p p − p0
1.3 K=ρ Assume K constant. Then ln(ρ/ρ0) =
∂ρ K
p − p0 81.7 × 106
∴ ρ = ρ0 exp = 1025 kg · m−3 exp
2.34 × 109
= 1061 kg · m−3
1.4 µ 2 10−5 N s m−2 3
ρ= = = 1.333 kg · m−
ν 15 × 10−6 m2 · s−1
p 1.013 × 105 N · m−2 259.2 J kg−1 K−1
R
= = = · ·
1.333 kg · m−3 × 293.15 K
ρT
8310
∴M= = 32.06
259.2
1.5 µ = νρ = 400 × 10−6 m2 · s−1 × 850 kg · m−3 = 0.34 Pa · s
0.12 m · s−1
Velocity gradient −1
= = 1200 s
0.1 × 10−3 m
Area = π 0.2 × 1.2 m2 = 0.754 m2
Force = 0.754 m2 × 0.34 Pa · s × 1200 s−1 = 307.6 N
, 2 Solutions manual
1.6 ∂u ∂u
Total force on plate = Area × µ +
∂y side A ∂y side B
0.15 m s−1
+ 0.15 m · s
2 −1
= (0.25 m) × 0.7 Pa · s 0.006 m 0.019 m
= 1.439 N
1.7 For annulus, radius r, width δr
Velocity ωr
Force Area µ = 2πrδrµ
= × ×
Clearancec
µω
∴ Torque = Force × r = 2πr3δr
c
∫ R
µω π R4µω
Total torque = 2π r3 dr =
0 c 2c
−1
π( 0.1 m) 0.14 Pa s × 2π × 7 rad s
4
= = 7.44 N · m
2 × 0.00013 m
1.8
2γ 2 × 0.073 N · m−1
p= = = 36.5 Pa
d 0.004 m
1.9 h 4γ cos θ 4 × 0.073 N · m−1 × 1
= =
ρgd 1000 kg · m−3 × 9.81 N · kg−1 × 0.005 m
= 0.00595 m = 5.95 mm
1.10 4 × 0.377 N · m−1 × cos 140◦
h
=
(13.56 − 1)1000 kg · m−3 × 9.81 N · kg−1 × 0.006 m
= −1.563 mm
1.11 Re udρ 4Qρ 4 × 0.0025 m3 · s−1 × 900 kg · m−3 1508
= = =
µ πdµ =
π 0.05 m × 0.038 N · s · m−2
2000µ2000 × 0.038 N · s · m−2
u= = 1.689 m · s−1
dρ −3
=
0.05 m × 900 kg · m
1.12 Re 4Qρ 4 × 0.01 m3 · s−1 430 Laminar
= = = ∴
πdµ π 0.08 m × 370 × 10−6 m2 · s−1
