Question

What is meant by streamline flow? State the equation of continuity. Write the properties of ideal fluid. Establish Bernoulli’s equation as applied to an ideal fluid.

Answer 1

Hint: Streamline flow is the one in which there are no turbulent velocity fluctuations. A streamline is a path of imaginary particles within the fluid that are carried along with it. The streamlines are fixed in a steady flow, and fluid travels in a smooth and regular path. This means that the flow properties like velocity, pressure, etc at each point remain constant.

Complete step-by-step solution:
To define streamline flow, think of the laminar flow consisting of laminae or thin layers, all parallel to each other. In a streamline motion, these layers of water are flowing on top of each other at different speeds and there is no mixing between layers.
Equation of continuity defined as the product of the cross product of the cross sectional area of the pipe and the velocity of the fluid at any given point
The properties of ideal fluid are:
Its flow is irrational and there is no turbulence in the flow.
It's non-viscous.
Its flow is steady and its density is constant.
Bernoulli’s equation as applied to an ideal fluid.
We make the following assumptions for the bernoulli's equation to be used.
The flow must be steady
The flow must be incompressible
Friction by viscous forces must be negligible.
Bernoulli's equation can be written as
$\dfrac{{{v}^{2}}}{2}+gz+\dfrac{p}{\rho }$ = constant
$v$ is the fluid flow speed at a point on a streamline ,$g$ is the acceleration due to gravity.
$z$ is the elevation of the point above a reference plane.
$p$ is the pressure at the chosen point.
$\rho $ is the density of the fluid at all points in the fluid.

Note: No fluid is totally incompressible whereas in practice the general qualitative assumptions still hold for real fluids . one should notice that in bernoulli's theorem, it is given that the velocity of every particle of liquid across any cross section is uniform which is not correct because the velocity of the particle is different in different layers.