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Bernoulli’s theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow and is the basis for many engineering applications.
Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.
Water is flowing through a horizontal tube. The pressure of the liquid in the portion where velocity is 2 m/s is 2 m of Hg. What will be the pressure in the portion where velocity is 4 m/s?
We know that Pv remains constant for any fluid and for non compressible fluids like water we get that Pv is always constant.
Also as 76cm of Hg = 10^{5} Pa
We get 2m Hg = 200/76 x 10^{5} Pa
Thus from conservation of Pv, we get that
2 x 200/76 x 10^{5} = 4 x P
Thus we get P = 100/76 x 10^{5}
Thus we get P = 1.31 x 10^{5}
Air is streaming past a horizontal airplane wing such that its speed is 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of the air is 1.3 kg/m^{3}and the wing is 10 m long and has an average width of 2 m, then the difference of pressure on the two sides of the wing is
Applying Bernoulli's principle, we have
P_{1}+1/2ρv_{1}^{2}=P_{2}+1/2ρv_{2}^{2}
⇒P_{2}−P_{1}=1/2ρ (v2/1−v2/2)
⇒ΔP=1/2×1.3× (1202−90^{2})
⇒ΔP=0.65× (120+90) × (120−90)
⇒ΔP=0.65×210×30=4095Pa
In which of the following types of flows is the Bernoulli’s theorem strictly applicable:
In the houses far away from the municipal water tanks often people find it difficult to get water on the top floor. This happens because
Every foot of elevation change causes a 0.433 PSI change in water pressure. If your pipe is going downhill add 0.433 PSI of pressure per vertical foot the pipe goes down. If the pipe is going uphill subtract 0.433 PSI for every vertical foot the pipe goes up.
Water is flowing through a pipe under constant pressure. At some place the pipe becomes narrow. The pressure of water at this place:
We know that the continuity theorem says that if the cross sectional area of the water flow decreases, the speed must increase to maintain the volume of water flown. And according to Bernoulli's principle if the speed of water flow increases , then the pressure must decrease.
Water is flowing through a horizontal pipe in streamline flow at the narrowest part of the pipe:
In streamline flow, the product of cross section area and velocity remains constant (equation of continuity). So in the narrowest part of the pipe velocity is maximum.
And from Bernoulli's theorem, we know that the sum of potential energy, kinetic energy and pressure energy remains constant. Since pipe is horizontal potential energy is equal at all the points. So the narrowest part of pipe pressure (pressure energy) will be minimum because velocity (kinetic energy) is maximum in the narrowest part.
To which type of fluid is the Bernoulli’s theorem applicable:
Bernoulli's theoremBernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.
Bernoulli’s principle is based on the conservation of:
Bernoulli's principle can even be derived from the principle of conservation of energy. Bernoulli's principle states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline.
Hence D is the correct answer.
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