Horizontal disk of mass M is constrained horizontally, but is free to move verti

Question

Horizontal disk of mass M is constrained horizontally, but is free to move vertically. A jet of fluid strikes the disk from below. The jet leaves the nozzle at initial speed Vo. The fluid jet decelerates to velocity V1 before it hits the plate due to gravity on the jet. The plate sits at an equilibrium height of ho above the jet exit plane. At the equilibrium position the net force on the plate is 0. a) Apply Bernoulli equation between control surfaces 0 and 1 to find an equation for the fluid velocity V1. b) Apply the integral mass conservation equation between control surfaces 0 and 1 to find an equation for the area of the fluid jet striking the plate A1. c) Apply the integral momentum equation to find an equation for the equilibrium height ho.

Explanation / Answer

v1 = sqrt.(2*delta p/density) v1 = [ 2 (p2 - p1) / ? ] ^1/2 where, p = static pressure (relative to the moving fluid) (Pa) ?= density (kg/m3) v = flow velocity (m/s) g = acceleration of gravity (m/s^2) v1 = [ 2 Pa / (kg / m^3) ] ^1/2 v1 = [ 2 (N / m^2) / (kg / m^3) ]^1/2 v1 = [ 2 N m / kg]^1/2 v1 = [( kg m/s^2 ) m /kg ] ^1/2 v1 = m^2 /sec^2 ] ^1/2 v1 = m/ sec So, the equation is dimensionally consistent.

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