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Preeti Dabral 2 years, 6 months ago
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy.
To prove Bernoulli's theorem, consider a fluid of negligible viscosity moving with laminar flow. as shown in Figure.
Let the velocity, pressure and area of the fluid cloumn be p1, v1 and A1 at Q and p2, v2 and A2 at R. Let the volume bounded by Q and R move to S and T where QS = L1, and RT = L2
If the fluid is incompressible:
The work done by the pressure difference per unit volume = gain in kinetic energy per unit volume + gain in potential energy per unit volume. Now:
A1L1 = A2L2
Work done is given by:
W = F {tex}\times{/tex} d = p {tex}\times{/tex} volume
{tex}\Rightarrow{/tex} Wnet = p1 - p2
{tex}\Rightarrow{/tex} K.E = {tex}\frac{1}{2}{/tex}mv2 = {tex}\frac{1}{2}{/tex}V {tex}\rho{/tex}v2 = {tex}\frac{1}{2}{/tex}{tex}\rho{/tex}v2 ({tex}\because{/tex} V = 1)
{tex}\Rightarrow{/tex} K.Egained = {tex}\frac{1}{2} \rho\left(v_{2}^{2}-v_{1}^{2}\right){/tex}
P1 + {tex}\frac{1}{2} \rho v_{1}^{2}{/tex} + {tex}\rho{/tex}gh1 = P2 + {tex}\frac{1}{2} \rho v_{2}^{2}{/tex} + {tex}\rho{/tex}gh2
{tex}\therefore{/tex} P + {tex}\frac{1}{2} \rho v^{2}{/tex} + {tex}\rho{/tex}gh = const.
For a horizontal tube
{tex}\because{/tex} h1 = h2
{tex}\therefore{/tex} P + {tex}\frac{1}{2} \rho v^{2}{/tex} = const.
Therefore, this proves Bernoulli's theorem. Here we can see that if there is an increase in velocity there must be a decrease in pressure and vice versa.
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Preeti Dabral 2 years, 6 months ago
vi = the initial velocity of an object measured using m/s. Therefore, the work-energy principle states that: The total work done by all the forces acting on a particle or the work of the resultant force F(in subscript resultant) is equivalent to the change in kinetic energy of a particle.
Posted by Sourav Mishra 2 years, 6 months ago
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Preeti Dabral 2 years, 6 months ago
Pascal's principle, also called Pascal's law, in fluid (gas or liquid) mechanics, statement that, in a fluid at rest in a closed container, a pressure change in one part is transmitted without loss to every portion of the fluid and to the walls of the container.
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Preeti Dabral 2 years, 6 months ago
The statement is wrong. The earth moves around the sun because of the gravitational force of the sun on the earth. This force acts along the radius of the orbit of the earth towards its center. At every point during the motion, the the direction of velocity (or direction of displacement) is always perpendicular to the force.
Thus, {tex}\theta {/tex} = 90o and
Work done, W = FS cos {tex}\theta {/tex} = FS cos90° = 0.
Hence, sun does no work on earth.
Posted by Chandan Mandal 2 years, 6 months ago
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Preeti Dabral 2 years, 6 months ago
- The expansion of water when it is cooled from 4oC to 0oC is known as anomalous expansion of water.
- Hope's experiment is used to demonstrate the anomalous expansion of water.
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Preeti Dabral 2 years, 6 months ago
Newton's law of gravitation, statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.
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Preeti Dabral 2 years, 6 months ago
Simple harmonic motion is an oscillatory motion in which the particle's acceleration and force are directly proportional to its displacement from the mean location at each point. It is a special case of oscillatory motion.
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