hi friends, i have a doubt regarding bernoulli's theorem so please if anyone knows it then share here........ it is said or proved by bernoulli that velocity is inversely proportional to pressure and whenever the cross sectional area of pipe decreases, then veolcity increases so pressure decreases.................. but i have a doubt that as per the definition of pressure, pressure is inversely proportional to area. so according to pressure definition, whenever area decreases pressure increases......... but bernoulli said pressure decreases because velocity increase.................... so can anyone please tell me that who is correct and why???? waiting for reply...........
Both the concepts are correct but we cont use it simultaneously,like in gas laws where pressure and volume both are directly proportional to temperature ,but pressure and volume are inversely proportional to each other.In bernoulli thoerm fluid flow in pipe with constant energy.To conserve the mass,velocity decrease with increase in area resulting in decrease of kinetic energy.At the expense of K.E ,pressure (pressure energy) increase.
P=F/A.....by this equation u might have understood that pressure is inversely proportional to area.
but this inverse relation is valid only if there is no kinetic energy component
if there is a kinetic energy component i.e. the fluid is in motion than bernoulli's principle must be applied
it happens as follow
Pressure is force per unit area, we can write the work done as force times volume of the liquid, where volume is area time distance travelled perpendicular to the force:
Therefore the volume of fluid under pressure has a potential energy equal to its volume times the pressure. Now we can move on to consider a fluid moving through a pipe with a change in cross-section. From the principle of the conservation of mass we know that the volume of fluid flowing through any cross-section must be the same. So if we slice the pipe at the large cross section we can calculate the volume flowing through it to be, density * velocity * cross-section area. At the smaller cross section we have a similar equation. Setting these two equal to each other yields:
As the cross-sectional area decreases, the velocity of the fluid increases.
Now from the law of conservation of energy, the energy of the fluid at these two cross-sections must also be equal. When the velocity increases in the narrow cross section, the fluid's kinetic energy increases. To compensate for this increase, the potential energy due to fluid pressure must drop
Pressure is also decreasing.Actually p=F/A,pressure is inversely proportional to area only when force is constant.Here force is not constant,but varying as area and height of cross section are are varying.