The question is ill-defined. In what system are you looking for such a relation? The answers above (the correct ones, at least) pertain to different systems. In thermal systems made of particulates (molecules, etc.) the pressure originates in the velocities of the particles hitting against the container walls and imparting momenta to it. This is the basis of pressure in the first place.
In a wide range of fluids the pressure (in fact the entire stress tensor) is often a function of velocity and in low reynolds numbers it is linear in it.
There are other systems where velocity is related to pressure, so please qualify on your question.
if you are using a pitot-static to measure flow velocity, it is for low Mach numbers a relationship of the dynamic pressure Pd=.5*rho*V2
dynamic pressure is the difference between total and static pressure at the pitot-static head
Exactly i agree with Fernando. I would like to add that the dynamic pressure is true when the input velocity is vanish.
There is a pressure, Volume, Temperature, relationship: PV = nR T
T in kelvins.
Simply, P=F/A=Force /Area=ma/A= mass*acceleration/Area=mv/t*A=
Mass*Velocity/time*Area= velocity is directly related to pressure
For steady-state in a flowing "ideal" incompressible inviscid fluid (e.g. the pressure and kinetic energy changes dwarf any energy losses by internal fluid friction), the sum
1/2* rho v**2 + P + rho* g * z =Constant
where rho is the fluid density, P is the pressure at a position x,y,z, g is the gravitational constant, and z is the height in the direction of gravitational force
at each and every spatial position in the fluid flow.. This is equivalent to conservation of energy. Most of the other answers above amount to a specialized application of this equation under particularized boundary conditions/geometries.
Strictly speaking, the Bernoulli equation above does not apply to a compressible flow (e.g. the ideal gas mentioned in a remark) although it can be applied approximately where viscous effects can be neglected (complex to generalize) and the velocity is very small compared to the speed of sound. It is also possible to extend the Bernoulli equation to non-static conditions (e.g. transient flow) when the approximations can be satisfied.
The ideal gas law mentioned above does not derive from Bernoulli's equation (it is an equation of state for a *compressible* fluid ), nor does a relationship between velocity and cross-sectional area in the flow (e.g. v*A=Constant is a geometrical constraint in certain circumstances, and does not follow from Bernoulli's equation). Finally, Bernoulli's equation is a very specialized case of the Navier Stokes equations which apply to generalized fluid flow. Where the fluid has viscosity or is compressible the constitutive fluid property(s) equations (e.g. rho(P,T, etc) and other things must be taken into account. Also please be aware that there exist other simplified fluid flow equations that apply under different circumstances (e.g. potential flow where at leastinertial terms and viscosity are both negligible).
PV = nRT is a ideal gas equation. idea gas obeys the maxwellian distributions. temperature of gas is nothing the average energy of gas particles. it means T of gas is directly related to the average velocity of gas particles. v = sqrt(KT/m). hence P is also related to the velocity of gas particles . P is directly proportional to square of average velocity of gas particles. it means P is related to the velocity.
PV=nRT is the definition of an ideal gas equation of state. Sirvi's remark about velocity pertains to the relation between classical thermodynamics and statistical mechanics. It has little (arguably almost nothing) to do with fluid flow (hydrodynamics).
The original questioner asked about "pressure and velocity", NOT pressure and temperature (or volume), so the question appeared to be about Fluid Mechanics, NOT thermodynamics. In thermodynamics, P (pressure) and T (Temperature) are intensities that can be fixed *independently* of one another, but a material equation of state can constrain the degrees of freedom (as in a phase diagram). Sirvi is dead wrong about the average velocity- simply consider that the average velocity of gas particles in a 1A cylinder of N2 moving at 0.5c (1/2 speed of light), the gas *molecules* (not particles) in the cylinder have a *directed* velocity of about 0.5c, regardless or cylinder temperature (please duck!).
Fluid flow is described by the Navier-Stokes equations. The Bernoulli equation mentioned by others is an approximation where viscosity is neglected (but please see earlier remarks about potential folow etc. where other terms are neglected, ie.potential flow). Where thermal effects are significant (e.g. heat flow, temperature, compressibility), heat transfer equations and material equations of state must included and solved simultaneously.
The question is ill-defined. In what system are you looking for such a relation? The answers above (the correct ones, at least) pertain to different systems. In thermal systems made of particulates (molecules, etc.) the pressure originates in the velocities of the particles hitting against the container walls and imparting momenta to it. This is the basis of pressure in the first place.
In a wide range of fluids the pressure (in fact the entire stress tensor) is often a function of velocity and in low reynolds numbers it is linear in it.
There are other systems where velocity is related to pressure, so please qualify on your question.
Pressure may or may not depend on velocity. Unless one states pressure from gases, liquids or solids, supplemented with static or dynamic, the question is very unclear. As an example, a liquid column of height h, density d will exert a pressure hdg even if there is no velocity. For gases, the pressure is related to velocity as square of velocity and for solids it is different.
Pressure and velocity are related through momentum equation .....
Arivu Che
Its an interesting question "pressure and velocity relationship". there is no one simple answer to this as u have not defined state fluid ??? compressible or incompressible???
People above have stated Bernoulli's eq or PV= nRT as answer, I am going to explain it another way
Remember 3 equations; Continuity, Momentum and Energy
Velocity is present in continuity, in Momentum & in energy equations while pressure is present in momentum (where velocity is also) and energy equation. Pressure is also present in energy equation along with volume and temperature.
From assumption of incompressible fluid (no friction) the continuity equation becomes called Bernoulli equation. while inorder to define a state of gas or its mixture in the energy equation, PV=nRT relationship is used as constitutive equation to solve energy equation.
Hope this serve your purpose but I think your question is not complete !!
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