Mr. Education

Turbines It is defined as, " component which extract energy off the flowing fluid " . Torque is exerted by the fluid on the rotor in its direction of rotation. The shaft power generated is available to drive generator or other devices. There are two types of Hydraulic Turbines: Impulse Turbines  Reaction Turbines 1. Impulse Turbines It is defined as, " The jet hits the Pelton wheel buckets, gets deflected, thus resulting in the change of the momentum " . Water is supplied from a high head. Large gravitational potential head which is converted into high velocity head. Penstock    →   Water moves down through the conduit. Working: High speed stream  →  further accelerated  →  through nozzle  →  produce greater velocity jet (convert static pressure into dynamic pressure). Analysis of Impulse Turbine 2. Reaction Turbines The fluid fills the space (blade, guide, rotor) completely through which it flows. Pressure, velocity and angular mom...

Turbomachinery It is defined as, " a dynamic fluid machine that adds energy to or extracts energy from the fluid " . Mechanical energy of rotation (rotation)   ← Transfer →    fluid flow energy . Mainly deals with two turbomachine pumps and turbine. Pumps (which require power source to operate) : Which adds energy to the working fluid. Usually a motor exerts a torque by using blades to force the fluid to move. Turbines (which is the source of power) : Which extracts energy from the working fluid. Fluid pushes the machine and produce shaft power. Classification On The Basis Of Flow Direction Turbomachines are classified on the basis of flow directions: Radial Flow machine    ↔   fluid flows in radial direction. Axial Flow machine    ↔    fluid flows along component axis. Mixed Flow machine    ↔   some machine have both radial and axial components. Working Principle During the fluid-blade interaction, eithe...

Moment of Momentum Equation " The rate of change of angular momentum of a system is equal to the net torque acting on the system (only valid for fixed mass and inertial frame of reference) " . Linear Momentum    ↠   Determine the relationship between the linear momentum of flow streams and the resultant forces. Angular Momentum    ↠   Determine the involvement of moment of linear momentum of the flow streams and rotational affects. Applications of Moment of Momentum Equation: Used to determine the torque applied by water . Analysis of the flow problem in centrifugal pump and turbine (i.e. Turbomachinery ). When to use Moment of Momentum equation: 1-dimensional flow. Steady or steady-in-the-mean cyclical flows. Only the components resolved along the axis of rotation will be taken into consideration. References: Material from Class Lectures + Book named Fundamentals of Fluid Mechanics by Munson, Young & Okiishi's (8th Edition) + my knowledge....

Momentum Integral Boundary Layer Equation for a Flat Plate Karman Solution (alternate method)  ↠  approx. closed form solution. Boundary layer theory  ↠  determination of drag (due to shear force)  ↠  using differential equation for laminar boundary layer flow (no exact solution)  ↠  alternate approx. method. Ques: How to solve Boundary layer? There are two solutions: By Blasius Solution    ↠   limited to laminar boundary layer and for a flat plate only (without a pressure gradient). By Momentum Integral Equation    ↠   used to obtain approx. information on boundary layer growth for the general case ( laminar or turbulent boundary layers with or without pressure gradient ). The flow entering the CV at the leading edge of the plate is uniform while the velocity of the flow leaving the CV varies from the upstream velocities at the edge of the boundary layer to zero velocity on plate. Drag on a flat plate is ...

Fluid Flow It is characterized by a freely growing boundary layer surrounded by an outer flow region that involves small velocity and temperature gradients. There are 2 types of fluid flow: External Flow    ↠   Fluid flow when the object is completely surrounded by the fluid. Internal Flow    ↠   Flow which are bounded by walls or fluid interfaces. Consider 2 other flows: Boundary Layer Flow    ↠   High Reynold's number flow around streamlines bodies without flow separation. Bluff Body Flow    ↠   Flow around bluff body with flow separation. Testing   ↠  Wind tunnel testing of model airplanes , building . Three general body characteristics : 2D Bodies    ↠   Infinitely long and of constant cross-sectional size and shape. Axisymmetric Bodies    ↠   Formed by rotating their cross-sectional shape about the axis of symmetry. 3D Bodies    ↠   M...

Conservation of Linear Momentum or Navier-Stokes Equation Applying Reynold transport theorem, Navier-Stokes Equation is for: Unsteady Non-Linear  2nd Order Partial Differential Equation Incompressible Flow Problem in solving NSE : Non-linearity due to Convective Acceleration terms . No general schemes for solving non-linear partial DE. Four unknowns (3 velocity components, 1 pressure)   Use above 3 equations. Use Incompressible Continuity equation. Application of NSE : Solved for several simple flow conditions. Used to describe complex flows. Applications of Navier-Stokes Equation 1. Steady, Laminar Flow between Fixed Parallel Plates 2. Couette Flow It is defined as, " Laminar flow of viscous fluid in the space between two parallel plates (one of which is moving relative to the other) " . Flow is driven by: Viscous drag force acting at the fluid. Applied pressure gradient parallel to the plates. Application are: Hydro-static lubrication Viscosity pumps Turbine Applied to Jo...

Fluid Element Kinematics We need to know inlet and outlet conditions  ⇋    Integral or CV Analysis or No flow properties . We need to follow fluid particles  ⇋  Flow domain or Differential analysis . Particles undergo four types of motion considering mass remain same: Translation Rotation Linear Deformation (have its volume changed) Angular Deformation (shape change) Ques: How fluid flows (i.e. all four types of motion)? All these motion take place all at a time because of difference in velocities (evidence: velocity profile in a pipe is look like parabolic i.e. velocity change). OR Pressure due to the fluid or wall friction changes. Linear Motion & Deformation Angular Motion & Deformation For  Pure rotation   ⇋  Ý = 0  &  Pure angular deformation   ⇋  ω = 0. Rate of Translation and Rotation Vorticity It is defined as, " curl of velocity vector OR Twice the angular velocity of fluid " . て = 0  ⇋  fl...