Chapter 3: Control Volume Analysis Part 11

In this video, the concepts of hydraulic grade line and energy grade line are discussed as graphical representations of the energy components in the Bernoulli equation. The definitions and applications of these concepts are explained.

Hydraulic Grade Line and Energy Grade Line

• The hydraulic grade line (HGL) and energy grade line (EGL) are graphical representations of the energy components in the Bernoulli equation.

• The HGL is a plot of the height of the pressure head plus the elevation head relative to an arbitrary reference point.

• The EGL is a plot of the total energy content, including velocity head, pressure head, and elevation head.

• Both lines provide insight into energy transformations in a piping system.

Application to Frictionless Flows

• Initially, frictionless Bernoulli-type flows are considered where there are no viscosity or energy losses.

• The concepts of HGL and EGL are applied to these idealized flows.

• The steady flow energy equation is used to describe these flows.

Application to Real Flows

• Real flows with head losses and pressure losses are then considered.

• Examples include flow across a valve and flow through a pump where energy is added.

• The concepts of HGL and EGL are applied to these realistic flows described by the steady flow energy equation.

Importance in Chapter Three

• In textbooks, hydraulic grade line and energy grade line concepts are usually presented early in Chapter 3 (around section 3.2).

• However, in this video series, their presentation is delayed until late in the chapter after understanding the steady flow energy equation.

Reviewing Bernoulli Equation

• Before discussing HGL and EGL concepts, a brief review of the Bernoulli equation is provided.

• Each term in the Bernoulli equation represents height or head, which is the energy content of the flow per unit weight.

• The kinetic energy term represents velocity head, the pressure term represents pressure head, and the elevation term represents elevation head.

Definitions of HGL and EGL

• The HGL is a plot of the height of the pressure head plus the elevation head relative to an arbitrary reference point.

• The EGL is a plot of the total energy content, including velocity head, pressure head, and elevation head.

• Both lines are graphical representations of the energy components in the Bernoulli equation.

By understanding hydraulic grade line and energy grade line concepts, engineers can gain insights into energy transformations in piping systems. These concepts are applicable to both idealized frictionless flows and real flows with losses.

Energy Grade Line and Hydraulic Grade Line

In this section, the concept of energy grade line and hydraulic grade line is discussed. The difference between the two lines and their significance in understanding flow behavior is explained.

Energy Grade Line and Hydraulic Grade Line

• The energy grade line (EGL) represents the total energy content per unit weight of fluid along a flow path.

• EGL = Z + P/gamma + V^2/(2g)

• It remains constant in flows where the energy grade lines are constant.

• The hydraulic grade line (HGL) represents the sum of elevation head (Z) and pressure head (P/gamma).

• HGL = Z + P/gamma

• The difference between EGL and HGL is the velocity head (V^2/(2g)).

• In real flows with viscous losses, such as those involving pumps, the energy grade line is a more useful descriptor than the hydraulic grade line.

• The hydraulic grade line increases in the flow direction because of the conversion of kinetic energy into pressure energy.

• As flow moves downstream, with a gradual increase in pipe diameter, velocity decreases due to continuity, resulting in less kinetic energy and approaching similarity between HGL and EGL.

Example: Frictionless Flow through Venturi Meter

This section discusses an example of frictionless flow through a venturi meter. The concept of hydraulic grade line and energy grade line for this type of flow is illustrated.

Frictionless Flow through Venturi Meter

• A venturi meter can be used to measure flow rate in a pipe by creating a constriction that increases fluid velocity.

• In frictionless flow through a venturi meter:

• The hydraulic grade line remains constant until reaching the constricted section where cross-sectional area decreases.

• The energy grade line is constant throughout the flow.

• The difference between EGL and HGL is the velocity head.

• At the inlet, there is a small difference between EGL and HGL due to velocity head.

• At the throat, where maximum velocity occurs, there is a maximum difference between EGL and HGL.

• In ideal frictionless flow with equal pipe diameters at both ends, pressure decreases towards the throat, resulting in complete recovery of hydraulic grade line height.

Actual Flow through Venturi Meter

This section discusses actual flow through a venturi meter, which involves viscous losses. A preview of an experiment using a venturi meter in lab number 4 is provided.

Actual Flow through Venturi Meter

• In real viscous flow through a venturi meter:

• Cross-sectional area gradually reduces to a minimum at the throat, causing an increase in fluid velocity.

• Downstream from the throat, cross-sectional area increases and velocity decreases.

• In this type of flow:

• The hydraulic grade line rises less due to pressure losses compared to ideal frictionless flow.

• Pressure at point 3 will be lower than at point 1 in real flows due to pressure losses.

• Lab experiments can measure hydraulic grade line height using pedometers and compare it with predictions based on Bernoulli's equation for ideal inviscid flow.

This summary covers only a portion of the transcript.

New Section

This section provides an introduction to the water tank system and the overflow pipe. The flow rate through the system can be controlled using a hand valve on the outlet.

Introduction to Water Tank System

• There is a continuous supply of water to the tank.

• The pipe seen above is an overflow pipe.

• Water level in the tank is maintained at a certain height, causing continuous overflow.

• A venturi meter is attached to the bottom of the tank.

New Section

This section explains the setup for Lab 4, which involves using pedometers and blue dye in the flow. The hand valve on the outlet allows control over the flow rate.

Lab 4 Setup

• Seven pedometers are used in this experiment.

• Blue dye is added to visualize flow heights (not present in actual lab).

• A hand valve on the outlet controls the flow rate.

New Section

A video presentation of Lab 4, demonstrating how pedometer levels change with varying flow rates through a venturi meter.

Video Presentation of Lab 4

• Valve is initially closed, resulting in equilibrium between pedometer levels and fluid in tank.

• Opening valve causes significant changes in pedometer levels.

• Steady-state hydraulic grade line observed when flow stabilizes.

• Flow is turned off, returning pedometers to original levels.

New Section

Analysis of hydraulic grade line and energy grade line based on results from Lab 4 experiment with venturi meter.

Analysis of Hydraulic Grade Line and Energy Grade Line

• Hydraulic grade line represents fluid levels in tops of pedometers.

• Minimum pressure occurs at throat of venturi meter, where maximum velocity is present.

• Energy grade line slopes downward in flow direction due to energy losses from viscosity and turbulence.

• In contrast to ideal flow, complete recovery of pressure head is not achieved.

New Section

Discussion on hydraulic grade line and energy grade line for a complex piping system with a tank, pipeline, pump, valve, nozzle, and fluid jet.

Hydraulic Grade Line and Energy Grade Line for Complex Piping System

• Hydraulic grade line represents pressure head above centerline of pipe.

• Energy grade line represents total energy per unit weight of fluid.

• Both lines slope downward in flow direction due to energy losses from viscosity and turbulence.

• Pump adds energy to overcome head loss in long pipelines.

New Section

Conclusion discussing the differences between hydraulic grade line and energy grade line in various scenarios.

Differences Between Hydraulic Grade Line and Energy Grade Line

• Hydraulic grade line represents pressure head while energy grade line represents total energy per unit weight of fluid.

• In some cases, both lines coincide (e.g., at tank where velocity is low).

• Slopes of both lines are downward in flow direction due to energy losses from viscosity and turbulence.

New Section Understanding Energy Losses in Fluid Flow

In this section, the speaker discusses energy losses associated with fluid flow and explains how pressure head is converted into velocity head.

Energy Losses in Fluid Flow

• Turbulence in pipes causes energy losses.

• Valves contribute to head loss.

• At the end of a pipe, a nozzle converts remaining pressure head into velocity head.

• The hydraulic grade line falls towards the center of the pipe.

New Section Interesting High-Speed Photography of Fluid Flow

The speaker shares an unrelated but fascinating video showcasing high-speed photography of fluid flow dynamics.

High-Speed Photography of Striking a Match

• Salir photography reveals density variations in fluids.

• The video shows incredible complexities of flow when striking a match.

• The video is about two and a half minutes long and becomes more interesting as it progresses.

Please refer to the video for the complete experience as it speaks for itself.