UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
THERMO-FLUIDS ASSIGNMENT 1
Semester 1 Assignment 01 — 2026
⋄
Module Code: TFL4801
Module Name: Thermo-Fluids
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for TFL4801 Thermo-Fluids
at the University of South Africa.
,UNISA | TFL4801 Thermo-Fluids Assignment 1 — 2026
Question 1: Ideal vs Real Fluids, Compressibility, and Bernoulli’s Equation
Fluid mechanics rests on a clear understanding of how fluids behave under applied forces.
The distinction between ideal and real fluids forms the conceptual foundation from which
governing equations like Bernoulli’s theorem are derived (Munson, Young and Okiishi, 2013).
1.1 Ideal Fluid vs Real Fluid
An ideal fluid is a theoretical construct. It is assumed to be completely incompressible,
meaning its density does not change with pressure, and it has zero viscosity, meaning it of-
fers no internal resistance to flow. No fluid in nature behaves this way entirely, but the model
is useful for simplifying complex flow analysis. When a fluid is treated as ideal, shear stresses
between adjacent layers are assumed to be absent.
A real fluid, by contrast, possesses viscosity. As layers of a real fluid move past one another
at different velocities, tangential shear stresses are generated at the interface. These stresses
dissipate energy, which is why pressure drops occur along pipelines and why pump power is
required to maintain flow. Water, oil, and air are all real fluids, each with measurable dynamic
viscosity (Cengel and Cimbala, 2018).
Table 1: Comparison of Ideal and Real Fluids
Property Ideal Fluid Real Fluid
Viscosity Zero Finite, positive value
Compressibility Incompressible Can be compressible
Shear stress None Present when velocity gradients
exist
Energy losses None Losses due to friction and tur-
bulence
Existence Hypothetical All real-world fluids
1.2 Compressibility of Fluids
Compressibility describes how much a fluid’s volume (and therefore density) changes in re-
sponse to an applied pressure. Liquids such as water are treated as incompressible in most
engineering analyses because their bulk modulus is very high; a pressure change of several hun-
dred bar produces only a tiny change in volume (less than 0.5% for water). Gases, however,
are highly compressible. The density of air changes appreciably even at moderate pressure
variations. The compressibility of a fluid is characterised by the bulk modulus of elasticity
Page 1 of 16
, UNISA | TFL4801 Thermo-Fluids Assignment 1 — 2026
K:
dp dp
K = −V =ρ (1)
dV dρ
where V is volume, p is pressure, and ρ is density. A high value of K means the fluid resists
compression strongly (Munson et al., 2013).
1.3 Bernoulli’s Theorem for Steady, Incompressible Flow
Bernoulli’s theorem states that for a steady, inviscid, incompressible flow along a streamline,
the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit
volume remains constant at every point along that streamline (White, 2016):
1
p + ρV 2 + ρgz = constant (2)
2
where p is static pressure (Pa), ρ is fluid density (kg/m3 ), V is flow velocity (m/s), g is gravi-
tational acceleration (m/s2 ), and z is elevation above a datum (m).
1.4 Derivation of Bernoulli’s Equation from Euler’s Equation
Euler’s Equation of Motion Along a Streamline
Euler’s equation is Newton’s second law applied to an inviscid fluid element along a streamline
direction s. Consider a small fluid element of cross-sectional area dA, length ds, and density ρ
moving along a streamline as shown in Figure 1.
∂p
p dA p+ ∂s ds dA
dm = ρ dA ds streamline
ds
datum z
z + dz
Figure 1: Fluid element along a streamline for Euler equation derivation
Applying Newton’s second law along the streamline direction s:
X
Fs = dm · as (3)
Page 2 of 16
College of Science, Engineering and Technology
⋄
THERMO-FLUIDS ASSIGNMENT 1
Semester 1 Assignment 01 — 2026
⋄
Module Code: TFL4801
Module Name: Thermo-Fluids
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for TFL4801 Thermo-Fluids
at the University of South Africa.
,UNISA | TFL4801 Thermo-Fluids Assignment 1 — 2026
Question 1: Ideal vs Real Fluids, Compressibility, and Bernoulli’s Equation
Fluid mechanics rests on a clear understanding of how fluids behave under applied forces.
The distinction between ideal and real fluids forms the conceptual foundation from which
governing equations like Bernoulli’s theorem are derived (Munson, Young and Okiishi, 2013).
1.1 Ideal Fluid vs Real Fluid
An ideal fluid is a theoretical construct. It is assumed to be completely incompressible,
meaning its density does not change with pressure, and it has zero viscosity, meaning it of-
fers no internal resistance to flow. No fluid in nature behaves this way entirely, but the model
is useful for simplifying complex flow analysis. When a fluid is treated as ideal, shear stresses
between adjacent layers are assumed to be absent.
A real fluid, by contrast, possesses viscosity. As layers of a real fluid move past one another
at different velocities, tangential shear stresses are generated at the interface. These stresses
dissipate energy, which is why pressure drops occur along pipelines and why pump power is
required to maintain flow. Water, oil, and air are all real fluids, each with measurable dynamic
viscosity (Cengel and Cimbala, 2018).
Table 1: Comparison of Ideal and Real Fluids
Property Ideal Fluid Real Fluid
Viscosity Zero Finite, positive value
Compressibility Incompressible Can be compressible
Shear stress None Present when velocity gradients
exist
Energy losses None Losses due to friction and tur-
bulence
Existence Hypothetical All real-world fluids
1.2 Compressibility of Fluids
Compressibility describes how much a fluid’s volume (and therefore density) changes in re-
sponse to an applied pressure. Liquids such as water are treated as incompressible in most
engineering analyses because their bulk modulus is very high; a pressure change of several hun-
dred bar produces only a tiny change in volume (less than 0.5% for water). Gases, however,
are highly compressible. The density of air changes appreciably even at moderate pressure
variations. The compressibility of a fluid is characterised by the bulk modulus of elasticity
Page 1 of 16
, UNISA | TFL4801 Thermo-Fluids Assignment 1 — 2026
K:
dp dp
K = −V =ρ (1)
dV dρ
where V is volume, p is pressure, and ρ is density. A high value of K means the fluid resists
compression strongly (Munson et al., 2013).
1.3 Bernoulli’s Theorem for Steady, Incompressible Flow
Bernoulli’s theorem states that for a steady, inviscid, incompressible flow along a streamline,
the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit
volume remains constant at every point along that streamline (White, 2016):
1
p + ρV 2 + ρgz = constant (2)
2
where p is static pressure (Pa), ρ is fluid density (kg/m3 ), V is flow velocity (m/s), g is gravi-
tational acceleration (m/s2 ), and z is elevation above a datum (m).
1.4 Derivation of Bernoulli’s Equation from Euler’s Equation
Euler’s Equation of Motion Along a Streamline
Euler’s equation is Newton’s second law applied to an inviscid fluid element along a streamline
direction s. Consider a small fluid element of cross-sectional area dA, length ds, and density ρ
moving along a streamline as shown in Figure 1.
∂p
p dA p+ ∂s ds dA
dm = ρ dA ds streamline
ds
datum z
z + dz
Figure 1: Fluid element along a streamline for Euler equation derivation
Applying Newton’s second law along the streamline direction s:
X
Fs = dm · as (3)
Page 2 of 16
