it does ? so we have a change in pressure between two points in the hose, so the velocity is not constant ?Lnewqban said:Yes.
No. Continuity demands that velocity be constant because there's nowhere else for the water to go.samy4408 said:it does ? so we have a change in pressure between two points in the hose, so the velocity is not constant ?
that makes sense thanks a lot!russ_watters said:No. Continuity demands that velocity be constant because there's nowhere else for the water to go.
Note, with the standard/ideal Bernoulli equation there is no loss, but in the real world there is (due to friction).
That's only true in a viscous flow. Bernoulli's equation does not apply in that situation without modification for viscous losses.Lnewqban said:That energy consumed by friction comes from the internal energy of the fluid in the way of static pressure, since the flow remains constant and height does not change.
If you could measure velocity and static pressure between two distant points, you would see that the value of velocity remains the same, but the value of static pressure downstream is lower than the one upstream.
Please, see:
https://www.tec-science.com/mechanics/gases-and-liquids/pressure-loss-in-pipe-systems/
That is the reason for the need of a circulating pump in a closed loop of constant height: you need to increase the pressure of the fluid between the end and the beginning of the loop by transferring mechanical energy from the pump into the fluid.
Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and elevation of a fluid in a closed system. It states that the sum of the kinetic energy, potential energy, and pressure energy of a fluid remains constant along a streamline.
Bernoulli's equation can be derived from the principles of conservation of mass, momentum, and energy. It involves simplifying the Navier-Stokes equations, which describe the motion of fluids, and applying the assumptions of steady, incompressible, and inviscid flow.
Bernoulli's equation has many practical applications in engineering and everyday life. It is used to calculate the lift and drag forces on an airplane wing, the flow rate in a pipe, and the pressure in a venturi meter. It also explains the phenomenon of lift in airfoils and the functioning of carburetors.
Bernoulli's equation is based on several assumptions, such as steady, incompressible, and inviscid flow, which may not hold true in all situations. It also does not take into account factors such as turbulence, viscosity, and compressibility, which can significantly affect the behavior of fluids.
Bernoulli's equation is a manifestation of the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of fluid flow, the total energy of the fluid remains constant, but it can be converted between different forms, such as kinetic, potential, and pressure energy.