Fluid Mechanics PDF

**CONSERVATION** **OF** **ENERGY** REPORTER: ***De Ocampo. Eljane A.*** ***BSED SCIENCE 3A*** **HYDRAULIC GRADE LINE (HGL) AND ENERGY GRADE LINE (EGL)** The Energy Grade Line (EGL) and Hydraulic Grade Line (HGL) are important concepts in fluid mechanics and hydrology, particularly in analyzin...

**CONSERVATION** **OF** **ENERGY** REPORTER: ***De Ocampo. Eljane A.*** ***BSED SCIENCE 3A*** **HYDRAULIC GRADE LINE (HGL) AND ENERGY GRADE LINE (EGL)** The Energy Grade Line (EGL) and Hydraulic Grade Line (HGL) are important concepts in fluid mechanics and hydrology, particularly in analyzing flow in pipes, open channels, or hydraulic systems. They help visualize how energy is distributed in a fluid system. **ENERGY GRADE LINE (EGL)** The **Energy Grade Line** represents the total mechanical energy (per unit weight) of the fluid at any point in a system. This energy includes potential energy (due to height), kinetic energy (due to velocity), and pressure energy. It is often convenient to represent the level of mechanical energy graphically using *heights* to facilitate visualization of the various terms of the Bernoulli equation. This is done by dividing each term of the Bernoulli equation by *g* to give A blue text on a white background Description automatically generated Each term in this equation has the dimension of length and represents some kind of **"head"** of a flowing fluid as follows: - *P/pg* is the **pressure head**; it represents the height of a fluid column that produces the static pressure *P*. - *V2/2g* is the **velocity head**; it represents the elevation needed for a fluid to reach the velocity *V* during frictionless free fall. - *z* is the **elevation head**; it represents the potential energy of the fluid. Also, *H* is the **total head** for the flow. Therefore, the Bernoulli equation is expressed in terms of heads as: *The sum of the pressure, velocity, and elevation heads along a streamline is constant during steady flow when compressibility and frictional effects are negligible*. The EGL is always above the fluid surface, indicating the total energy available. The energy grade line (EGL) represents the total head height. **HYDRAULIC GRADE LINE (HGL)** The **Hydraulic Grade Line** represents the height to which water would rise in a piezometer (a tube used to measure pressure) at any point in the fluid system. It accounts for the elevation and pressure heads, but not the velocity head. The hydraulic grade line (HGL) height represents the sum of the elevation and static pressure heads, \ [\$\$z + \\frac{p}{\\text{pg}}\$\$]{.math.display}\ In a static pressure tap attached to the flow conduit, liquid would rise to the HGL height. For open-channel flow, the HGL is at the liquid free surface. The HGL shows how much of the fluid\'s energy is due to pressure and elevation, which determines whether a system has sufficient pressure for delivery or needs pumping. Understanding the relationships between the HGL and EGL helps engineers analyze flow conditions, energy losses, and design efficient systems to control fluid motion. Efficient system designs aim to minimize energy losses between these lines, ensuring optimal performance. **STAGNATION PRESSURE** **Stagnation pressure** is the pressure a fluid would have if it were brought to a complete stop (stagnated) isentropically (without any losses due to heat, friction, or other dissipative effects). It represents the total pressure at a point where the fluid velocity is zero. Stagnation pressure is the sum of two components: 1. Static pressure : This is the actual pressure exerted by the fluid while it is in motion, but not considering its velocity. 2. Dynamic pressure : This is the pressure due to the fluid\'s velocity, representing its kinetic energy per unit volume. A white background with black text Description automatically generated Stagnation pressure is also referred to as total pressure because it combines both the static and dynamic pressures. It is the pressure measured at a point where the fluid flow has been brought to rest (e.g., in front of a pitot tube in an aircraft). **Applications:** - **Aerospace and Aerodynamics**: Stagnation pressure is critical in determining the forces acting on aircraft surfaces. It is measured using pitot tubes, which help determine airspeed by comparing stagnation pressure to static pressure. - **Piping Systems**: In pipelines, stagnation pressure helps engineers assess pressure changes when fluids are stopped or slowed down, ensuring that systems are designed to handle these pressure levels. - **Compressible Flow**: In high-speed flow systems, such as nozzles and wind tunnels, stagnation pressure is used to calculate changes in fluid properties when the fluid is decelerated to rest. Stagnation pressure is always higher than the static pressure for a moving fluid. **FLOW IN A CURVED PATH** Flow in a curved path refers to the motion of fluid along a path that is not straight, such as around bends in a pipe, through a curved channel, or over curved surfaces. When fluid flows along a curved path, the fluid particles experience changes in velocity direction, which leads to several distinct phenomena, such as the development of centrifugal forces, pressure variations, and changes in the velocity profile. **KEY CONCEPTS:** **Centripetal Force** When fluid flows along a curved path, each particle is subject to a centripetal force that pulls it toward the center of the curve. This force is necessary to keep the fluid in a curved trajectory. The centripetal force is proportional to the fluid\'s mass, velocity, and the curvature of the path. Mathematically:  **Pressure Distribution** In curved flow, a **pressure gradient** develops across the flow cross-section. The pressure is higher on the outer edge of the curve and lower on the inner edge due to the need to provide the centripetal force to keep the fluid on the curved path. The pressure difference between the inner and outer walls ensures that the fluid particles experience the necessary centripetal acceleration. **Secondary Flow** In curved channels or pipes, secondary flows can develop, which are small circulations of fluid perpendicular to the main flow direction. These are often seen in ducts, rivers, and centrifugal pumps, and are caused by the imbalance between the pressure gradient and the centrifugal force. **Applications:** Flow in curved paths is common in many engineering applications, including piping systems with bends, open channels, rivers, turbomachinery (such as pumps and turbines), and aircraft wing surfaces. **Examples of Flow in a Curved Path:** **Piping Systems:** Elbows and bends in pipelines force the fluid to follow a curved path, creating pressure drops and possible flow separation. **Rivers:** In river bends, water flows faster on the outer bank (erosion occurs) and slower on the inner bank (sedimentation occurs), creating the classic meandering pattern. **Centrifugal Pumps:** These pumps use curved flow paths to impart energy to fluids, utilizing the centrifugal force to move the fluid outward. **Cyclones:** In gas or liquid cyclones, the fluid follows a curved, spiral path, with the centrifugal force separating particles based on density. **FORCED VORTEX** A forced vortex is a type of vortex where the fluid rotates as a solid body, with each particle having the same angular velocity about a central axis. This is different from a free vortex, where the angular velocity decreases as the distance from the center increases. In a forced vortex, the fluid behaves like a rigid body, meaning every point in the fluid rotates at the same angular velocity. This type of motion is called **solid body rotation** because the velocity of fluid particles increases linearly with the distance from the center of rotation. **Examples of Forced Vortex:** - **Centrifugal Pumps and Turbines**: In these machines, fluid is forced to rotate by external forces, creating a forced vortex. The blades impart angular momentum to the fluid, causing it to move in circular paths. - **Rotating Cylinders or Containers**: When fluid is placed in a rotating container, the fluid near the walls spins faster than the fluid near the center, creating a forced vortex. **FREE VORTEX (IRROTATIONAL VORTEX)** In a free vortex, the fluid particles move in circular paths without the application of external torque or mechanical forces. The fluid's angular momentum is conserved, and as a result, the tangential velocity of the particles decreases as the distance from the center increases. The fluid motion in a free vortex is not driven by any external mechanical force. The flow is caused by the initial motion of the fluid and conserves angular momentum. Despite the swirling motion, the fluid particles in a free vortex do not rotate about their own axes, so the flow is considered irrotational. The vorticity, which measures local rotation, is zero everywhere except at the singularity point (the vortex center). **Examples of Free Vortex:** - Water draining through a sink (whirlpool). - Tornadoes or cyclones (atmospheric free vortex). - Vortex created by swirling smoke rings.