shanewatson said:In Bernoulli's equation, why the work on fluid at the lower end of the pipe is taken as negative?
please explain why the force is negative to displacement at the lower end?
The convention is to consider upwards movment and upwards forces as positive, and downwards movement and downwards forces as negative. Gravitational potential energy is the negative of the work done by gravity, so GPE increases (more positive or less negative) as an object moves upwards, and decreases as an object moves downwards. The potential term in Bernoulli's equation follows the same rule, but it's potential energy per unit volume (density x gravitational acceleration x height).shanewatson said:please explain why the force is negative to displacement at the lower end?
Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height of a fluid in a steady flow. It states that as the velocity of a fluid increases, the pressure decreases and vice versa.
Bernoulli's equation has many practical applications. It is used in designing aircraft wings, calculating water flow in pipes, and understanding blood flow in the human body. It is also used in industries such as oil and gas, aviation, and hydropower.
Bernoulli's equation is derived from the conservation of energy principle. It states that the total energy of a fluid in a steady flow remains constant, and this energy is divided into kinetic energy, potential energy, and internal energy.
Bernoulli's equation assumes that the fluid is incompressible, non-viscous, and the flow is steady and irrotational. These assumptions may not hold true in all real-life situations, and therefore, the results obtained from Bernoulli's equation may not be accurate.
In aerodynamics, Bernoulli's equation is used to explain the lift force on an aircraft wing. As the air flows over the curved upper surface of the wing, its velocity increases, causing a decrease in pressure and creating a pressure difference that results in lift force.