Lecture 4 Pressure distribution in fluids. Pressure and pressure gradient. Hydrostatic pressure 1

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Basic Principles of Fluid Mechanics Mass conservation => Lei de Newton: => 2

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Methods for Fluid Mechanics

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Chapter 2 Concept of pressure and pressure gradient, Hydrostatics and centripetal force. Lei de Newton: Acceleration as the result of the applied forces.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Forces in Fluids Surface or volumetric (or mass) Surface forces can be normal (pressure) or tangential (friction) Tangential forces are always parallel to velocity. Their equation can be complex if velocity is not parallel to any reference axis.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Pressure is a scalar Could be different in one point?

Engenharia do Ambiente Mecânica dos Fluidos Ambiental In a fluid at rest: Esta conclusão é independente de θ.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Pressure Gradient It will be shown that the pressure gradient can generate acceleration, but not the pressure by itself.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Pressure force resultant

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Force resultant (including friction and weight)

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Summing up

Engenharia do Ambiente Mecânica dos Fluidos Ambiental General equation At rest the fluid has null velocity and so are its derivatives. The pressure is hydrostatic. Se a aceleração vertical for nula a pressão continua a ser hidrostática.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Hydrostatic pressure If the vertical axes (zz) points downwards gravity acceleration is positive, otherwise is negative.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Hydrostatics

Engenharia do Ambiente Mecânica dos Fluidos Ambiental If was constant:

Engenharia do Ambiente Mecânica dos Fluidos Ambiental In case of gas

Engenharia do Ambiente Mecânica dos Fluidos Ambiental

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Hydrostatic Forces Objectif: Compute the hydrostatic force over flat and curve surfaces and the application point (pressure centre).

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Força Hidrostática

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Computing using former knowledge

Engenharia do Ambiente Mecânica dos Fluidos Ambiental OU

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Pressure Centre (Measured from the gravity centre)

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Pressure Centre (x coordinate) On surfaces with vertical simetry CP lays on the axis.

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Resumo