physicsfluid-dynamics

Why does a decrease in cross-sectional area increase the pressure


When the cross section of the flow tube decreases, the flow speed increases, and therefore the pressure decreases.

can someone explain to me why this is true, i would think that as the cross section decreases the pressure would also increase .


Solution

  • This is related to "Continuity Equation" of fluid mechanisam.(Assuming fluid as incompressible)

    if we have two cross-sections of areas A1 and A2 having velocities V1 and V2 respectively .Then according to continuity equation

    A1*V1=A2*V2 or we can write

    V2=(A1*V1)÷A2

    V2 Is inversly proportional to the A2.

    so velocity increases as the area decreases.

    further we have a theorem in fluid mechanics called "Bernouli's theorem".

    which states that the sum of all energies at any cross-section is constant.

    So if the velocity(i.e kinetic energy) increases at any section there will be decrease in pressure(i.e pressure energy)