1. Fluid mechanics 3.1 – key points
A stationary fluid cannot withstand a shear stress but deforms under the action of a shear.
Fluids can be treated as continuous in time and space.
A fluid is shaped by external forces (i.e. a fluid takes up the shape of its container)
Gauge pressure equals the absolute pressure minus the atmospheric pressure, or
Absolute pressure equals the gauge pressure plus the atmospheric pressure.
Unit 3
An Introduction to Mechanical Engineering: Part One

2. Fluid mechanics 3.1 – key points
Absolute pressure (relative to vacuum) and gauge pressure (relative to atmospheric pressure) are both used in engineering.
Temperatures must be in kelvin in the perfect gas equation.
To convert from C to K, add
Pressure in a fluid is associated with molecular motion.
When pressure is constant over an area, F = pA .
Unit 3
An Introduction to Mechanical Engineering: Part One

3. Fluid mechanics 3.1 – key points
The perfect gas equation of state can be used to obtain gas properties.
Liquids can usually be treated as incompressible but gases cannot.
Unit 3
An Introduction to Mechanical Engineering: Part One

4. Fluid mechanics 3.1 Learning summary
By the end of this section you will be able to:
calculate the density of an object from its mass and volume;
know the difference between and calculate gauge and absolute pressure;
use the perfect gas equation of state to calculate the properties of gases.
Unit 3
An Introduction to Mechanical Engineering: Part One

5. Fluid mechanics 3.2 – key points
In a fluid at rest, pressure acts equally in all directions.
Where a fluid is in contact with a surface, the pressure gives rise to a force acting perpendicular to the surface.
In a fluid at rest, pressure is constant along a horizontal plane.
In a fluid at rest, pressure increases with depth according to the relationship p = gh
The pressure at the base of a column of fluid of depth h is equal to the pressure at the top + gh
Unit 3
An Introduction to Mechanical Engineering: Part One

6. Fluid mechanics 3.2 – key points
Pressures can be measured by manometers.
Surface tension can affect the readings of manometers.
On a submerged horizontal surface the pressure is constant and the centre of pressure is also the centre of area (centroid).
On a submerged vertical surface the pressure increases with depth and the centre of pressure is below the centroid.
Unit 3
An Introduction to Mechanical Engineering: Part One

7. Fluid mechanics 3.2 – key points
On an inclined flat or curved surface the horizontal force and its line of action is equal to the horizontal force on the vertical projection of the inclined or curved surface.
On an inclined flat or curved surface, the vertical force is equal to the weight of the volume of water vertically above the surface and its line of action passes through the centre of gravity of that volume.
Unit 3
An Introduction to Mechanical Engineering: Part One

8. Fluid mechanics 3.2 – key points
A body fully immersed in a fluid experiences a vertical upwards force equal to the weight of the volume of fluid displaced.
A floating body displaces its own weight in liquid.
Unit 3
An Introduction to Mechanical Engineering: Part One

9. Fluid mechanics 3.2 Learning summary
By the end of this section you will be able to:
determine the pressure at any depth below the surface of a liquid at rest;
calculate the pressure difference indicated by a manometer;
calculate by integration the magnitude and line of action of the force due to fluid static pressure on a submerged, flat, horizontal or vertical surface;
evaluate the horizontal and vertical components of force on a submerged, inclined, flat or simple curved surface and determine the resultant force and line of action for some simple shapes;
calculate buoyancy forces on submerged and floating objects and determine the conditions for equilibrium.
Unit 3
An Introduction to Mechanical Engineering: Part One

10. Fluid mechanics 3.3 & 3.4 – key points
A steady flow is one that does not change with time.
A uniform flow is one where the properties do not vary across a plane or within a volume.
A one-dimensional flow is one where flow properties only vary in one direction.
An ideal (inviscid) fluid has no viscosity, and is incompressible. No real fluid is ideal but the simplification is valid in some situations.
Unit 3
An Introduction to Mechanical Engineering: Part One

11. Fluid mechanics 3.3 & 3.4 – key points
For a steady flow, the law of conservation of mass (continuity) means that the flow entering a volume must equal the flow leaving a volume.
The Euler equation is a differential equation for the flow of an ideal fluid.
The Bernoulli equation expresses the relationship between pressure, elevation and velocity in an ideal fluid for steady flow along a streamline.
The Bernoulli equation can be expressed in three ways, in terms of specific energy, pressure or head.
Unit 3
An Introduction to Mechanical Engineering: Part One

12. Fluid mechanics 3.3 & 3.4 – key points
The Bernoulli equation can be used for real fluids when losses due to friction are negligible and the fluid is incompressible.
Viscosity in a fluid creates frictional drag in a fluid flow.
The higher the viscosity of a fluid, the greater is the resistance to motion between fluid layers, and, for a given applied shear stress, the lower is the rate of shear deformations between layers
Unit 3
An Introduction to Mechanical Engineering: Part One

13. Fluid mechanics 3.3 & 3.4 – key points
There are two fundamental types of fluid flow laminar and turbulent. They can be characterized by the Reynolds number of the flow.
The steady flow energy equation can be applied to the flow of real fluids and leads to the extended Bernoulli equation that can be used to describe the losses resulting from viscous friction in a flow.
The Moody Chart can be used to estimate the frictional losses in pipe and duct flows.
The SFEE can be used to determine the performance of a pump needed in a pipe system.
Unit 3
An Introduction to Mechanical Engineering: Part One

14. Fluid mechanics 3.3 & 3.4 Learning summary
By the end of this section you will be able to:
calculate the mass flowrate of a steady flow in a pipe or duct;
understand the three forms of the Bernoulli equation;
be able to apply the Bernoulli equation to calculate flows in pipes including the performance of venturi, nozzle and orifice plate flow meters and a pitot-static probe;
calculate the drag forces created by viscosity in thin films between moving surfaces;
calculate the Reynolds number of flows in pipes and ducts and determine whether the flow is likely to be laminar or turbulent;
estimate the pressure losses in flows in pipes due to friction;
calculate the pressures and flows in simple single pipe systems accounting for losses due to friction in pipes and other components of pipe systems;
calculate the performance of a pump needed in a simple pipe flow system.
Unit 3
An Introduction to Mechanical Engineering: Part One

15. Fluid mechanics 3.5 – key points
The forces exerted by fluids when they change velocity and direction can be evaluated using the momentum equation derived from Newton’s second law of motion.
Control volumes are the easiest way to analyse momentum flow problems.
The linear momentum equation states that for a steady flow: The force in a particular direction on a control volume is equal to the rate of change in momentum of the fluid flowing in that direction.
Unit 3
An Introduction to Mechanical Engineering: Part One

16. Fluid mechanics 3.5 – key points
The force on the control volume is the sum of all the forces acting, including external pressure, gravity and structural forces from solid objects crossing the control volume boundaries.
Unit 3
An Introduction to Mechanical Engineering: Part One

17. Fluid mechanics 3.5 Learning summary
By the end of this section you will be able to:
calculate the forces generated when a fluid flow impinges on an object or is constrained to change direction.
Unit 3
An Introduction to Mechanical Engineering: Part One