rectilinear translation _ moving vessel _ advance engineering mathematics review
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Rotation _ Rotating Vessel _ Advance Engineering Mathematics ReviewTRANSCRIPT
Rectilinear Translation | Moving Vessel
Tags: force polygon constant acceleration horizontal motion inclined motion vertical motion fluid mass
Horizontal Motion
If a mass of fluid moves horizontally along a straight line at constant acceleration a, the liquid surface assume an angle θ with the horizontal, see figure
below.
For any value of a, the angle θ can be found by considering a fluid particle of mass m on the surface. The forces acting on the particle are
the weight W = mg, inertia force or reverse effective force REF = ma, and the normal force N which is the perpendicular reaction at the
surface. These three forces are in equilibrium with their force polygon shown to the right.
From the force triangle
Inclined Motion
Consider a mass of fluid being accelerated up an incline α from horizontal. The horizontal and vertical components of inertia force REF would be
respectively, x = mah and y = mav.
From the force triangle above
but a cos α = ah and a sin α = av, hence
Use (+) sign for upward motion and (-) sign for downward motion.
Vertical Motion
The figure shown to the right is a mass of liquid moving vertically upward with a constant acceleration a. The forces acting to a
liquid column of depth h from the surface are weight of the liquid W = γV, the inertia force REF = ma, and the pressure F = pA at
the bottom of the column.
Use (+) sign for upward motion and (-) sign for downward motion. Also note that a is positive for acceleration and negative for deceleration.
Submitted by Romel Verterra on December 13, 2012 - 11:53pm
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