Fluid Mechanics Report PDF

**CONSERVATION** **OF** **ENERGY** REPORTER: ***De Ocampo. Eljane A.*** **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 c...

**CONSERVATION** **OF** **ENERGY** REPORTER: ***De Ocampo. Eljane A.*** **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. **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). Stagnation pressure is always higher than the static pressure for a moving fluid. Stagnation pressure is a useful concept in fluid dynamics, particularly in the analysis of flow in nozzles, pipes, and around objects like aircraft wings. **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. 1. **Centrifugal Force** When fluid follows a curved path, the particles in the fluid experience a centrifugal force directed outward from the center of the curvature. This force is proportional to the square of the velocity of the fluid and inversely proportional to the radius of curvature of the path: The centrifugal force affects the distribution of pressure and velocity in the flow. Fluid particles on the outer side of the curve experience higher centrifugal forces, causing the pressure to be higher on the outer side and lower on the inner side. 2. **Pressure Gradient** Due to the centrifugal force, there is a pressure gradient across the curved path. Pressure is higher on the outer side (convex side) of the curve and lower on the inner side (concave side). This imbalance helps keep the fluid particles following the curve rather than flying off the path. 3. **Secondary Flow** In addition to the primary flow direction along the curve, secondary flows can develop due to the pressure gradient. These secondary flows are often in the form of spiral or vortex-like motions, where the fluid near the outer curve moves faster than the fluid near the inner curve. **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. **Example: Flow in a Curved Pipe** When fluid flows through a curved pipe, the centrifugal force pushes the fluid towards the outer wall, creating a higher pressure there. This can lead to a secondary flow pattern, where fluid near the walls moves inward along the inner curve, while the fluid near the center moves outward. **Example: River Bends** In rivers or open channels, water flows faster along the outer bank of a curve and slower along the inner bank, leading to erosion on the outer bank and deposition on the inner bank. This is an example of how flow in curved paths can shape natural environments. **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.