3. The tank shown has a parabolic curve gate at the bottom right side of length h perpendicular to the paper. The parabola has a vertex at the center of the hinge A. The parabola is defined by the equation in the X-Y coordinate system as shown. Neglecting the weight of the gate and the vertical reaction at the bottom end B of the gate, show the following if the unit weight of the liquid is y. (a) The magnitude of horizontal component of the hydrostatic force on the curve AB is 4.5yh³. 14 (b) The location of the horizontal component is the x axis. 17 h below (c)The magnitude of the vertical component of the hydrostatic force on the curve AB is yh³. 26 Liquid surfac 4h hinge 2h P

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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3. The tank shown has a parabolic curve gate at the bottom right side of length h
perpendicular to the paper. The parabola has a vertex at the center of the hinge A. The
parabola is defined by the equation in the X-Y coordinate system as shown. Neglecting
the weight of the gate and the vertical reaction at the bottom end B of the gate, show
the following if the unit weight of the liquid is y.
(a) The magnitude of horizontal component of the
hydrostatic force on the curve AB is 4.5yh³.
14
(b) The location of the horizontal component is ―h below
17
the x axis.
(c)The magnitude of the vertical component of the
hydrostatic force on the curve AB is yh³.
26
3
(e)The magnitude of the horizontal force P just to prevent the
opening is
yh³.
Liquid surface
27
(d) The location of the vertical component ish from the y axis is
26
124
3
4h
27
- h.
26
hinge
2h
Transcribed Image Text:3. The tank shown has a parabolic curve gate at the bottom right side of length h perpendicular to the paper. The parabola has a vertex at the center of the hinge A. The parabola is defined by the equation in the X-Y coordinate system as shown. Neglecting the weight of the gate and the vertical reaction at the bottom end B of the gate, show the following if the unit weight of the liquid is y. (a) The magnitude of horizontal component of the hydrostatic force on the curve AB is 4.5yh³. 14 (b) The location of the horizontal component is ―h below 17 the x axis. (c)The magnitude of the vertical component of the hydrostatic force on the curve AB is yh³. 26 3 (e)The magnitude of the horizontal force P just to prevent the opening is yh³. Liquid surface 27 (d) The location of the vertical component ish from the y axis is 26 124 3 4h 27 - h. 26 hinge 2h
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