Disclaimer: This content was created by a student who was influenced by the book Fluid Mechanics by Yunus A. Cengel and John M. Cimbala.
The Bernoulli equation states that the total energy of a fluid in a steady state flow is constant along a streamline. This total energy can be broken down into three components: pressure head, energy head, and elevation head.
P + (1/2) * ρ * v^2 + ρ * g * z = constant
- Pressure head: It is the height of the fluid in a piezometer above the pipe center, and it is directly proportional to the pressure of the fluid. It is measured in units of length, such as meters or feet. The pressure head term in the Bernoulli equation is represented as P/(ρ*g), where P is the pressure, ρ is the density of the fluid, and g is the acceleration due to gravity.
- Energy head: It is the velocity energy of the fluid, and it is directly proportional to the square of the fluid’s velocity. It is measured in units of length, such as meters or feet. The energy head term in the Bernoulli equation is represented as (v^2/2g), where v is the velocity of the fluid.
- Elevation head: It is the height of the fluid above a reference point, and it is directly proportional to the weight of the fluid. It is measured in units of length, such as meters or feet. The elevation head term in the Bernoulli equation is represented as z, where z is the height of the fluid above the reference point.
In the Bernoulli equation, the sum of the pressure head, energy head, and elevation head represents the total energy per unit weight of the fluid. It is this balance that the Bernoulli equation describes.
The Hydraulic Grade Line (HGL) and the Energy Grade Line (EGL) are important concepts in fluid mechanics that describe the behavior of fluids in pipe systems.
Hydraulic Grade Line (HGL)
A piezometer is a device that is used to measure the pressure of a fluid in a pipe by tapping into the pipe and measuring the height of the liquid in the piezometer. The liquid will rise to a height of P/(ρ*g) above the pipe center, where P is the pressure, ρ is the density of the fluid, and g is the acceleration due to gravity.
The hydraulic grade line (HGL) can be obtained by measuring the height of the liquid in the piezometer at different locations along the pipe and drawing a curve through these points. The HGL represents the elevation of the free surface of the fluid in the pipe, and it is the line at which the pressure of the fluid is equal to the atmospheric pressure.
The vertical distance of the liquid above the pipe center in the piezometer is a measure of the pressure within the pipe. The higher the liquid level in the piezometer, the higher the pressure within the pipe, and the lower the liquid level in the piezometer, the lower the pressure within the pipe.
If the fluid has an elevation height, z, the hydraulic grade line (HGL) represents the sum of the static pressure head and the elevation head.
Therefore, the HGL can be represented as:
HGL = P/(ρ*g) + z
Energy Grade Line (EGL)
A pitot tube is a device that is used to measure the static and dynamic pressure of a fluid in a pipe by tapping into the pipe and measuring the height of the liquid in the pitot tube.
The liquid would rise to a height of P/(ρ*g) + v^2/2g above the pipe center, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and v is the velocity of the fluid. This height represents the sum of the static pressure head and the dynamic pressure head.
The energy grade line (EGL) can be obtained by measuring the height of the liquid in the pitot tube at different locations along the pipe and drawing a curve through these points. The EGL represents the total energy per unit weight of the fluid, and it is the sum of the pressure head, velocity head, and elevation head of the fluid.
If the fluid also has an elevation head, z, the total head of the fluid, P/(ρ*g) + v^2/2g+z, is called the energy grade line (EGL).
