UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
TFL4801: Thermo-Fluids
Assignment 1 — First Semester, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
TFL4801
Module Code:
Thermo-Fluids
Module Name:
Assignment 1 – Fluid Mechanics
Assignment:
01
Assignment Number:
[DD Month 2026]
Due Date:
50
Total Marks:
Submitted in partial fulfilment of the requirements for TFL4801 — UNISA 2026
,UNISA | TFL4801 Thermo-Fluids Assignment 1 – 2026
Question 1: Ideal vs Real Fluids, Compressibility, and Bernoulli’s Theorem
Fluid mechanics rests on a set of idealised models that simplify real-world behaviour into
tractable mathematics. Two such models – the ideal fluid and Bernoulli’s equation – form the
backbone of introductory fluid analysis (Munson, Young and Okiishi, 2013:3).
1.1 Ideal Fluid and Real Fluid
An ideal fluid (also called a perfect fluid) is a theoretical fluid that is assumed to be com-
pletely inviscid and incompressible. It has zero viscosity, meaning there is no internal friction
between fluid layers, and its density remains constant regardless of the applied pressure. Be-
cause viscosity is absent, an ideal fluid cannot sustain shear stress – it transmits only normal
(pressure) forces. These assumptions make mathematical analysis far simpler, and solutions
derived for ideal fluids often serve as useful benchmarks for engineering calculations (Cengel
and Cimbala, 2018:48).
A real fluid, on the other hand, exhibits viscosity. Viscosity is the property of a fluid that
resists relative motion between adjacent layers; it is the source of internal friction and is re-
sponsible for energy losses in pipe flow. Real fluids are also slightly compressible, though for
liquids at moderate pressures the compressibility effect is small enough to neglect. The viscos-
ity of a real fluid generates a velocity gradient near solid walls (the boundary layer), causes
pressure drops along pipelines, and produces wake effects behind bluff bodies – none of which
appear in ideal-fluid theory (White, 2016:29).
Key Distinction
Ideal Fluid: Zero viscosity, incompressible, no shear stress. Used for theoretical
analysis.
Real Fluid: Finite viscosity, slightly compressible, shear stress present. Governs all
practical engineering flows.
1.2 Compressibility of Fluids
Compressibility is the measure of a fluid’s volume change in response to an applied pressure.
It is quantified by the bulk modulus of elasticity K:
Page 2 of 19
, UNISA | TFL4801 Thermo-Fluids Assignment 1 – 2026
Table 1: Comparison of Ideal and Real Fluids
Property Ideal Fluid Real Fluid
Viscosity Zero Finite (temperature-dependent)
Compressibility Incompressible Slightly compressible
Shear Stress None Present wherever velocity gradi-
ent exists
Boundary Layer Not formed Forms along all solid surfaces
Energy Losses None Present due to friction and
turbulence
dP
K = −V (1)
dV
where V is volume and P is pressure. Liquids such as water have a very high bulk modulus
(K ≈ 2.1 × 109 Pa), so they resist volume change strongly and are treated as incompressible
in most engineering problems. Gases are far more compressible – their bulk modulus equals
γP (where γ is the ratio of specific heats), meaning volume changes significantly with pressure.
A flow is treated as incompressible when the Mach number M a < 0.3 (Cengel and Cimbala,
2018:52).
1.3 Bernoulli’s Theorem
Bernoulli’s theorem states: For the steady, incompressible, inviscid flow of a fluid along
a streamline, the sum of static pressure, dynamic pressure, and hydrostatic pressure head
remains constant between any two points on that streamline (Munson et al., 2013:99).
Mathematically:
P V2
+ + z = constant (2)
ρg 2g
or equivalently in pressure form:
1
P + ρV 2 + ρgz = constant (3)
2
1.4 Assumptions for Bernoulli’s Equation
1. The flow is steady – fluid properties at any point do not change with time.
2. The fluid is incompressible – density ρ is constant.
3. The fluid is inviscid – viscous effects and energy losses are neglected.
Page 3 of 19
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
TFL4801: Thermo-Fluids
Assignment 1 — First Semester, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
TFL4801
Module Code:
Thermo-Fluids
Module Name:
Assignment 1 – Fluid Mechanics
Assignment:
01
Assignment Number:
[DD Month 2026]
Due Date:
50
Total Marks:
Submitted in partial fulfilment of the requirements for TFL4801 — UNISA 2026
,UNISA | TFL4801 Thermo-Fluids Assignment 1 – 2026
Question 1: Ideal vs Real Fluids, Compressibility, and Bernoulli’s Theorem
Fluid mechanics rests on a set of idealised models that simplify real-world behaviour into
tractable mathematics. Two such models – the ideal fluid and Bernoulli’s equation – form the
backbone of introductory fluid analysis (Munson, Young and Okiishi, 2013:3).
1.1 Ideal Fluid and Real Fluid
An ideal fluid (also called a perfect fluid) is a theoretical fluid that is assumed to be com-
pletely inviscid and incompressible. It has zero viscosity, meaning there is no internal friction
between fluid layers, and its density remains constant regardless of the applied pressure. Be-
cause viscosity is absent, an ideal fluid cannot sustain shear stress – it transmits only normal
(pressure) forces. These assumptions make mathematical analysis far simpler, and solutions
derived for ideal fluids often serve as useful benchmarks for engineering calculations (Cengel
and Cimbala, 2018:48).
A real fluid, on the other hand, exhibits viscosity. Viscosity is the property of a fluid that
resists relative motion between adjacent layers; it is the source of internal friction and is re-
sponsible for energy losses in pipe flow. Real fluids are also slightly compressible, though for
liquids at moderate pressures the compressibility effect is small enough to neglect. The viscos-
ity of a real fluid generates a velocity gradient near solid walls (the boundary layer), causes
pressure drops along pipelines, and produces wake effects behind bluff bodies – none of which
appear in ideal-fluid theory (White, 2016:29).
Key Distinction
Ideal Fluid: Zero viscosity, incompressible, no shear stress. Used for theoretical
analysis.
Real Fluid: Finite viscosity, slightly compressible, shear stress present. Governs all
practical engineering flows.
1.2 Compressibility of Fluids
Compressibility is the measure of a fluid’s volume change in response to an applied pressure.
It is quantified by the bulk modulus of elasticity K:
Page 2 of 19
, UNISA | TFL4801 Thermo-Fluids Assignment 1 – 2026
Table 1: Comparison of Ideal and Real Fluids
Property Ideal Fluid Real Fluid
Viscosity Zero Finite (temperature-dependent)
Compressibility Incompressible Slightly compressible
Shear Stress None Present wherever velocity gradi-
ent exists
Boundary Layer Not formed Forms along all solid surfaces
Energy Losses None Present due to friction and
turbulence
dP
K = −V (1)
dV
where V is volume and P is pressure. Liquids such as water have a very high bulk modulus
(K ≈ 2.1 × 109 Pa), so they resist volume change strongly and are treated as incompressible
in most engineering problems. Gases are far more compressible – their bulk modulus equals
γP (where γ is the ratio of specific heats), meaning volume changes significantly with pressure.
A flow is treated as incompressible when the Mach number M a < 0.3 (Cengel and Cimbala,
2018:52).
1.3 Bernoulli’s Theorem
Bernoulli’s theorem states: For the steady, incompressible, inviscid flow of a fluid along
a streamline, the sum of static pressure, dynamic pressure, and hydrostatic pressure head
remains constant between any two points on that streamline (Munson et al., 2013:99).
Mathematically:
P V2
+ + z = constant (2)
ρg 2g
or equivalently in pressure form:
1
P + ρV 2 + ρgz = constant (3)
2
1.4 Assumptions for Bernoulli’s Equation
1. The flow is steady – fluid properties at any point do not change with time.
2. The fluid is incompressible – density ρ is constant.
3. The fluid is inviscid – viscous effects and energy losses are neglected.
Page 3 of 19
