Fluid Mechanics
(18AS33): Video Lectures
Prof. Ashish Kumar Gupta
1
,Kinematics of fluid describes the fluid motion and its Fluid Kinematics
consequences without consideration of the nature of Analysis of Fluid Flow
forces causing the motion. Different approaches to study the fluid flows are-
Lagrangian method- Using Lagrangian method, the fluid motion is described by tracing
the motion of each particle constituting the flow.
Identities of the particles are made by specifying their initial position (spatial location) at
a given time. The position of a particle at any other instant of time then becomes a
function of its identity and time. It can be stated alternatively as-
X̅=X(x̅0,t0); x̅= xi+yj+zk. X̅ is the location vector of the particles at any given time, t. x̅0 is
the initial location of the particles at time t0. Alternatively it can be written as x =
x(x0,y0,z0,t), Similarly, one can write for motion along y and z-axis also.
Eulerian Method- This method is of greater advantage since it avoids the determination
of the movement of each individual fluid particle in all details. In this approach, the flow
variables, such as pressure, temperature or velocity of fluid particles are given as a
function of its position and time. Thus the flow variables are known at all points.
2
, Hence, we can write it as V=V(x, y, z, t); or p=p(x, y, z, t) Fluid Kinematics
T=T(x, y, z, t) etc. Analysis of Fluid Flow
Scalar and Vector Fields
Scalar: Scalar is a quantity which can be expressed by a single number representing its
magnitude. Example: mass, density and temperature. Example of scalar field-
Temperature distribution in a turbine blade.
Vector: Vector is a quantity which is specified by both magnitude and direction. Example:
Force, Velocity and Displacement. Example of vector field- velocity field of a flowing
fluid .
Variation of Flow Parameters in Time and Space- Flow parameters like pressure and
temperature and density along with flow velocity may vary from one point to another but
if it remains same at a given point with change in time, it is called as steady flow.
Flow parameters like pressure, temperature and density along with flow velocity may vary
from one point to another but if it varies at a given point with change in time, it is called
as unsteady flow.
3
, In Eulerian approach, for steady flow, the flow variables Fluid Kinematics
are given by V=V(x, y, z); or p=p(x, y, z) & T=T(x, y, z) etc. Analysis of Fluid Flow
For unsteady flow they are functions of time.
Uniform Flow
The flow is defined as uniform flow when in the flow field, the velocity and other flow
parameters do not change from point to point at any instant of time. Thus V=V(t); or
p=p(t) . Free stream is a special case of uniform flow which represents far away flows.
Non-Uniform Flow-
When the velocity and other hydrodynamic parameters changes from one point to another
the flow is defined as non-uniform.
Acceleration of a Fluid element- The velocity components u, v, w of the particle along
x, y and z directions respectively can then be written in Eulerian form as u = u (x, y, z, t),
v = v (x, y, z, t) and w = w (x, y, z, t). After an infinitesimal time interval Δt , let the
particle move to a new position given by the coordinates (x + Δx, y +Δy , z + Δz) with
velocities, u+Δu, v+Δv and w+Δw. So writing the Tailor series 4
(18AS33): Video Lectures
Prof. Ashish Kumar Gupta
1
,Kinematics of fluid describes the fluid motion and its Fluid Kinematics
consequences without consideration of the nature of Analysis of Fluid Flow
forces causing the motion. Different approaches to study the fluid flows are-
Lagrangian method- Using Lagrangian method, the fluid motion is described by tracing
the motion of each particle constituting the flow.
Identities of the particles are made by specifying their initial position (spatial location) at
a given time. The position of a particle at any other instant of time then becomes a
function of its identity and time. It can be stated alternatively as-
X̅=X(x̅0,t0); x̅= xi+yj+zk. X̅ is the location vector of the particles at any given time, t. x̅0 is
the initial location of the particles at time t0. Alternatively it can be written as x =
x(x0,y0,z0,t), Similarly, one can write for motion along y and z-axis also.
Eulerian Method- This method is of greater advantage since it avoids the determination
of the movement of each individual fluid particle in all details. In this approach, the flow
variables, such as pressure, temperature or velocity of fluid particles are given as a
function of its position and time. Thus the flow variables are known at all points.
2
, Hence, we can write it as V=V(x, y, z, t); or p=p(x, y, z, t) Fluid Kinematics
T=T(x, y, z, t) etc. Analysis of Fluid Flow
Scalar and Vector Fields
Scalar: Scalar is a quantity which can be expressed by a single number representing its
magnitude. Example: mass, density and temperature. Example of scalar field-
Temperature distribution in a turbine blade.
Vector: Vector is a quantity which is specified by both magnitude and direction. Example:
Force, Velocity and Displacement. Example of vector field- velocity field of a flowing
fluid .
Variation of Flow Parameters in Time and Space- Flow parameters like pressure and
temperature and density along with flow velocity may vary from one point to another but
if it remains same at a given point with change in time, it is called as steady flow.
Flow parameters like pressure, temperature and density along with flow velocity may vary
from one point to another but if it varies at a given point with change in time, it is called
as unsteady flow.
3
, In Eulerian approach, for steady flow, the flow variables Fluid Kinematics
are given by V=V(x, y, z); or p=p(x, y, z) & T=T(x, y, z) etc. Analysis of Fluid Flow
For unsteady flow they are functions of time.
Uniform Flow
The flow is defined as uniform flow when in the flow field, the velocity and other flow
parameters do not change from point to point at any instant of time. Thus V=V(t); or
p=p(t) . Free stream is a special case of uniform flow which represents far away flows.
Non-Uniform Flow-
When the velocity and other hydrodynamic parameters changes from one point to another
the flow is defined as non-uniform.
Acceleration of a Fluid element- The velocity components u, v, w of the particle along
x, y and z directions respectively can then be written in Eulerian form as u = u (x, y, z, t),
v = v (x, y, z, t) and w = w (x, y, z, t). After an infinitesimal time interval Δt , let the
particle move to a new position given by the coordinates (x + Δx, y +Δy , z + Δz) with
velocities, u+Δu, v+Δv and w+Δw. So writing the Tailor series 4
