• anonymous
In bernoulli's THEOREM! large area has high pressure and low speed,where as the formula of pressure is P=F/A?
MIT 8.01 Physics I Classical Mechanics, Fall 1999
  • Stacey Warren - Expert
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  • jamiebookeater
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  • TuringTest
Bernoulli's principle is a direct result of conservation of energy, and the formula for pressure you posted above.|dw:1329419515359:dw| Summing up the energy in the system we have\[E=K+U_g+W=\frac12mv^2+mgh+Fd\]subbing mass=density*volume, and distance=(volume)/(cross-sectional area):\[E=\frac12\rho Vv^2+\rho Vgh+F(\frac VA)=\frac12\rho Vv^2+\rho Vgh+(\frac FA)V\]\[=\frac12\rho Vv^2+\rho Vgh+pV\]divide by rho V, and note that energy per unit volume is a constant for an incompressible fluid.\[\frac{v^2}2+gh+\frac p\rho=\text{constant}\]
  • Mani_Jha
P=F/A is an equation of hydrostatics. That means, we use it only when the fluid is at rest. Try setting v=0 in the above equation, and u get the result that you would obtain from P=F/A. But due to motion, the pressure is less where velocity is more. This is because the fluid rushes out with a very high speed, creating a low pressure in that region where it leaves. Now, according to equation of continuity, the velocity is less where area is more(think that the fluid has a large room to move in). So, pressure there is more. This is not valid if the fluid is at rest.

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