## anonymous 4 years ago In bernoulli's THEOREM! large area has high pressure and low speed,where as the formula of pressure is P=F/A?

1. 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}$

2. 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.