Question

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A quarter - circle cylinderical gate with a length of 4m is placed in the side of a reservoir contanting water as shown in Figure 2 Determine the magnitude of the horizontal and vertical components of the force of the water on the gate (yw = 9810 nm) Water am k Gate Figure 2

Answer 1

While calculating horizontal force take care to calculate projected area of curved on vertical surface . Second point is to be taken care of vertical distance between center of gravity of projected area and free surface .

In vertical force calculation take care of volume of element upto free surface, supported by curved surface .

E E Projected Area projected Area of Gate C 1299991 4m As we know that houzontal jovce a surface Innmenged in water is equals to = SAX 1 Fronsonnel = Sg AX - where g-acceleration due to gravity = 9.81 = devinity of fluid here it water to = 1000 kg/m3 A= Projected Area of Tumenged Surface on ho veutical plane As we can see in figure the projected are of quaten unde with 3m radius and 4 m length will be rectangle of Cux 3 m² X is distance Center of gravity of projected Ared from free waten surface LLLLLL x = (6+1.5 m lason - Projected Area

S2 Page 2 now we have all the values = 1000 kg kom 9 = 9.81 m A = (3x4) m² (Projected Area och gate ou I veutical plane) x = veutical distance between free Surface and center of Gravity of projected Area As gate stoutes from 6m depth so X=(6 + 1,5) = 7.5m 1.5 m is the projected Area Centen of Gravity in sendical diretion, Fucs 1000x9-81X (3 xu) (7-5) Thorizontal Fi = 882900 N

free water sufia For veutical force on gate we will calculate volume of at AOPO STR Z element because Ventical dicuction force on Gate 3 = weight of juid supported apto (R=3m 7 af Gate free laten surface LD=6m Requered volume of elenail - (Area of A oz x 4 ) + (Area of PQRzx W 2 xu) + 6x 3X4 ) = 100.21m' - premmインブー [Area of quanten Ciule = x d² Freshed = weight of fluid eenent upto free Surface Fresh - Volume of element apto free Surface x S x g. Freka = 100.2 1x 1000x9,81 = 983691.21 N Arne