## Fundamentals of fluid mechanics

Hydrostatics is the study of fluids at rest.

Experiments on buoyancy, density, capillarity etc.; various methods of pressure measurement

##### Learning objectives/experiments

- study of buoyancy on a variety of bodies
- study of the density of liquids
- hydrostatic pressure, Pascal’s law
- communicating vessels
- determination of the centre of pressure

….

Investigation of fluid pressure on vessel walls

##### Learning objectives/experiments

- pressure distribution along an effective area in a liquid at rest
- lateral force of the hydrostatic pressure
- determination of the centre of pressure and centre of area
- determination of the resulting compressive force

Determining metacentre and buoyancy; rectangular frame cross-section

##### Learning objectives/experiments

- study and determination of
- buoyancy, centre of buoyancy
- centre of gravity, metacentre, stability
- heel

Comparison of two different frame shapes: hard chine and round bilge

##### Learning objectives/experiments

- comparison of two different frame shapes: hard chine and round bilge

Hydrodynamics is concerned with the study and description of fluids in motion. The main emphasis is the teaching of the conservation laws of mass, energy and momentum.

Visualisation of laminar and turbulent flow

##### Learning objectives/experiments

- visualisation of laminar flow
- visualisation of the transition zone
- visualisation of turbulent flow
- determination of the critical Reynolds number

Visualisation of laminar and turbulent flow

##### Learning objectives/experiments

- visualisation of
- laminar flow
- transition zones
- turbulent flow
- secondary flow in a pipe elbow

….

Measurement of laminar and turbulent flow

##### Learning objectives/experiments

- representation of the flow profile
- determination of local and averaged flow velocity
- effect of the Reynolds number on the flow profile
- recognise differences between laminar and turbulent flow formation
- pipe friction / shear stress

….

Flow around various drag bodies and incident flow of weirs

##### Learning objectives/experiments

- energy levels of the water when flowing through a flume with different obstacles
- investigation of the hydraulic jump
- Venturi flow rate measurement
- energy dissipation in the flume

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Static pressure and total pressure distribution along the Venturi nozzle

##### Learning objectives/experiments

- energy conversion in divergent/convergent pipe flow
- recording the pressure curve in a Venturi nozzle
- recording the velocity curve in a Venturi nozzle
- determining the flow coefficient
- recognising friction effects

Static pressure and total pressure distribution along the Venturi nozzle

##### Learning objectives/experiments

- energy conversion in divergent/convergent flow
- record the pressure curve in the Venturi nozzle
- determine the velocity curve in the Venturi nozzle
- qualitative evaluation of pressure losses
- identify influences of nozzle and diffuser on pressure loss

….

Demonstration of the principle of linear momentum; interchangeable deflectors with different deflection angles

##### Learning objectives/experiments

- demonstration of the principle of linear momentum
- study of the jet forces
- influence of flow rate and flow velocity
- influence of different deflection angles

Demonstration of the principle of linear momentum; interchangeable deflectors with different deflection angles

##### Learning objectives/experiments

- application of the momentum equation
- measurement of the jet forces
- investigate influencing variables of jet forces
- deflection angles
- nozzle pre-pressure

….

Flow around various drag bodies and incident flow of weirs; ink as contrast medium

##### Learning objectives/experiments

- how differently shaped weirs affect the flow
- visualisation of streamlines for flow incident to a weir
- visualisation of streamlines when flowing around various drag bodies

Investigation of flow around models in laminar, two-dimensional flow using ink as contrast medium

##### Learning objectives/experiments

- visualisation of streamlines in
- flow around drag bodies
- flow through changes in cross-section

- influence of sources and sinks

Investigation of cross-sectional changes in laminar, two-dimensional flow; visualisation using electrolytically generated hydrogen bubbles

##### Learning objectives/experiments

- visualisation of two-dimensional flows
- learning the concept of streamlines, flow lines and strike lines
- streamline course through an experimental section with changes in cross-section
- limits of potential flow
- friction

….

- friction

Relationship between cross-sectional area traversed and flow velocity

##### Learning objectives/experiments

- investigation of the continuity equation
- demonstration of conservation of mass
- identification of the influencing variables
- cross-sectional flow area
- pitch of the impellers

….

The flow from a tank can be regarded as both steady and transient. In the steady case the fill level, and thus the width of the jet, remains constant (e.g. discharge under a weir).

When the tank is emptying during the discharge process, it is in what is referred to as the transient state.

Determination of pressure losses and contraction coefficient for different outlet contours

##### Learning objectives/experiments

- study of the outlet jet (diameter, velocity)
- determination of pressure losses and contraction coefficient for different outlet contours
- determination of flow rate at different discharge heads

Recording the trajectory of the water jet at different outlet velocities

##### Learning objectives/experiments

- recording the trajectory of the water jet at different outlet velocities
- study of how the level in the tank affects the outlet velocity
- determination of the contraction coefficient for different contours and diameters
- comparison of the actual and theoretical outlet velocity

Recording the trajectory of the water jet and discharge coefficients at different outlet velocities

##### Learning objectives/experiments

- investigate how the level in the tank affects the outlet velocity
- apply Bernoulli’s equation
- compare determined and theoretical outlet velocity
- investigate outlet inserts with different diameters and inlet contours, determine pressure loss coefficients
- investigate how the outlet velocity and the pressure loss coefficient affect the trajectory of the water jet

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When flowing through a pipe the friction causes the pressure energy of the fluid to fall and the internal energy of the fluid to increase.

Influence of flow velocity on pressure loss, didactically successive pipe sections

##### Learning objectives/experiments

- pressure losses in pipes, pipe fittings and pipe elements
- how flow velocity affects pressure loss
- application of Bernoulli’s equation
- determine resistance coefficients
- opening characteristics of valve and ball valve

….

Pipe friction for laminar / turbulent flow, Reynolds number and pipe friction factor

##### Learning objectives/experiments

- using the Reynolds number in pipe flow
- determine critical Reynolds number
- calculate the Reynolds and pipe friction coefficient from measured data
- compare theoretical values with measured values
- investigate the influence of temperature

….

Friction losses in the inlet as well as with different pipe geometries and surface roughnesses

##### Learning objectives/experiments

- formation of the flow along the inlet section
- difference between hydraulically smooth and rough pipes
- difference between round pipe and rectangular cross-section
- distinction between laminar and turbulent flow
- determine pressure loss in laminar flow / turbulent flow

….

Flow processes on different structures in open and closed channel flows; losses at inlet and outlet

##### Learning objectives/experiments

- open channel
- flow over control structures: broad-crested weir, narrow-crested weir, ogee-crested weir with ski jump spillway, sill
- discharge under a gate
- hydraulic jump

- closed channel

….

Pressure losses at various piping elements and pipe networks; parallel and series connection of pipe sections

##### Learning objectives/experiments

- recording the calibration curve for pipe sections: pressure loss over flow rate
- pipe sections connected in parallel
- pipe sections connected in series
- combined series and parallel connection
- investigation of a closed circular pipeline

….

Determining the critical Reynolds number

##### Learning objectives/experiments

- measurements of the pressure loss in laminar flow
- measurements of the pressure loss in turbulent flow
- determining the critical Reynolds number
- determining the pipe friction factor
- comparing the actual pipe friction factor with the theoretical friction factor

Influence of flow velocity on pressure loss

##### Learning objectives/experiments

- pressure losses in pipes, piping elements and fittings
- how the flow velocity affects the pressure loss
- determining resistance coefficients
- opening characteristics of angle seat valve and gate valve
- familiarisation with various measuring objects for determining flow rate:

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In turbomachines the energy transfers between fluid and machine by means of flow forces.

Model of an impulse turbine with adjustable nozzle; determination of the efficiency

##### Learning objectives/experiments

- design and function of a Pelton turbine
- determination of torque, power and efficiency
- graphical representation of characteristic curves for torque, power and efficiency

Model of a reaction turbine with adjustable guide vanes; determination of the efficiency

##### Learning objectives/experiments

- design and function of a Francis turbine
- determination of torque, power and efficiency
- graphical representation of characteristic curves for torque, power and efficiency

Determining the characteristics of a typical centrifugal pump

##### Learning objectives/experiments

- familiarisation with operating behaviour and characteristics of a centrifugal pump through experiments
- recording the pump characteristic curve at a constant pump speed
- measuring the inlet and outlet pressure
- determining the flow rate

- recording the pump characteristics for different speeds

….

Characteristic curves and hydraulic power; comparison of operating modes

##### Learning objectives/experiments

- investigation of pumps in series and parallel configuration
- determining the head
- recording the pump characteristics
- determining the hydraulic power
- determining the operating point

Transient flow: the velocity of a fluid particle changes with the time and the position. Transient flows occur during discharge processes, during startup and shutdown processes of turbomachines or in the case of fluid oscillations and water hammer processes.

Investigation of formation, effect and function

##### Learning objectives/experiments

Transient flow conditions in pipe systems by means of experimentation

- demonstrating water hammer in pipes
- determining the wave propagation velocity in water
- understanding how a surge chamber works
- natural frequency in the surge chamber

Demonstration of the function of a rainwater retention basin and a storage lake

##### Learning objectives/experiments

- demonstrating transient drainage processes in two rainwater retention basins located one behind the other
- demonstrating transient drainage processes in two storage lakes located one behind the other
- recording oscillations of the water level in a surge chamber after water hammer
- recording and displaying water level fluctuations