Fig.B-19 Horizontal
and vertical components of the
hydrostatic force acting on an
element of a curved wall. A com-
ponent acting into any direction
is (because of the scalar charac-
ter of pressure ... Pascal law)
equal to product of pressure and
area of the projection of surface
element into the given direction.

well-known Archimedes law of lift force equal to weight of displaced liquid.
4) The case of a submersed body
Let us consider an element of body surface (Fig.B-19) and evaluate the pressure force components acting on it, in the horizontal direction and in the vertical direction . In the case of a body there will always be another surface element opposite to the originally considered one, having the same projected area. In the direction , where there is the same pressure in the same depth, the acting elementary forces on the original and opposite element
Fig.B-20
are of equal magnitude and of mutually opposing direction, so that they cancel each other. In the vertical direction ,
however, there is the difference in depths and this gives rise to pressure difference. Since the pressure acting on the bottom opposite element (Fig.B-20) is larger than on the top element, the net effect is a force acting in the vertical, upwards direction. By integrating these elementary forces, over the whole top surface of the body, above the curve k , the total lift is obtained. It is evident that it is equal in magnitude to the overall weight of the liquid displaced by the immersed body. If this magnitude is larger than the actual weight of the body, the body will rise towards the surface. Its upward motion continues even when part
Fig.B-21
of the body emerges from the liquid. The lift is then, of course, decreased (there is a decrease in the displacement by the part outside the liquid). In the end, the decreased lift becomes equal to the body weight and the upward motion stops - the body floats and its floating is stable. The hydrostatic centre in which the lift is acting is located in the centre of gravity of the displaced volume. Apart from the consideration of stability of vertical forces an important issue is the stability of moments: the force couple formed by and should generate a restoring moment which tends to dectease the tilt. As a measure of this rotational stability of ships, the metacentric height has been introduced. It is the distance between ship centre of gravity and athe metacentre measured along the symmetry line. The dependence of on tilt angle is usually evaluated by measurement performed on a finished ship. The tilt is generated by placing known load at a known distance


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This is page Nr. B08 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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