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yp = h” – ( H – d) = mL/ (ρgBD (d – D/2)) – ( H – d)

Using the equation for the centre of pressure, we can determine the equations

for the theoretical h” and centre of pressure

h = {{{D} ^ {2}} over {12} + {( d- {D} over {2} )} ^ {2}} over {( d- {D} over {2} )} +H-d

and yp = d – D/2 +

D

2

12(d−

D

2

)

Equipment

Figure 1 shows a general layout of the hydrostatic force apparatus. Water is

contained in a rectangular tank into which a quadrant tank is immersed. The

size of the quadrant tank and the related dimensions of the set-up are shown in

Figure 2. In Figure 2, C is the centroid of the projected area of the vertical face of

the quadrant tank. The centre of pressure of the vertical force acting on the

same vertical face is represented by the point P. The horizontal distance

between the pivot point (marked as a filled triangle) and the balance pan or

weight hanger is referred to as L. the vertical distance between the bottom of

the quadrant face and the pivot arm is known as H. The height and width of the

quadrant face is D and B, respectively. The approximate dimensions of these

variables are shown in the following table.

Length of Balance L 0.275m Distance from weight hanger to pivot

Quadrant to Pivot H 0.200m Base of quadrant face to pivot

Height of

Quadrant

D 0.100m Height of vertical quadrant face

Width of

Quadrant

B 0.075m Width of vertical quadrant face

In the set-up, the line of contact of the knife-edge pivot coincides with the

vertical face of the quadrant tank. Thus, of the hydrostatic forces acting on the

immersed quadrant, only the horizontal thrust acting on the vertical face of the

tank will exert a counter-clockwise moment about the knife-edge axis. In

addition to the quadrant clamping screw the balance arm incorporates a balance

pan, an adjustable counterbalance and an indicator which shows when the arm

is horizontal. This is important as a horizontal arm coincides with the condition

yp = h” – ( H – d) = mL/ (ρgBD (d – D/2)) – ( H – d)

Using the equation for the centre of pressure, we can determine the equations

for the theoretical h” and centre of pressure

h = {{{D} ^ {2}} over {12} + {( d- {D} over {2} )} ^ {2}} over {( d- {D} over {2} )} +H-d

and yp = d – D/2 +

D

2

12(d−

D

2

)

Equipment

Figure 1 shows a general layout of the hydrostatic force apparatus. Water is

contained in a rectangular tank into which a quadrant tank is immersed. The

size of the quadrant tank and the related dimensions of the set-up are shown in

Figure 2. In Figure 2, C is the centroid of the projected area of the vertical face of

the quadrant tank. The centre of pressure of the vertical force acting on the

same vertical face is represented by the point P. The horizontal distance

between the pivot point (marked as a filled triangle) and the balance pan or

weight hanger is referred to as L. the vertical distance between the bottom of

the quadrant face and the pivot arm is known as H. The height and width of the

quadrant face is D and B, respectively. The approximate dimensions of these

variables are shown in the following table.

Length of Balance L 0.275m Distance from weight hanger to pivot

Quadrant to Pivot H 0.200m Base of quadrant face to pivot

Height of

Quadrant

D 0.100m Height of vertical quadrant face

Width of

Quadrant

B 0.075m Width of vertical quadrant face

In the set-up, the line of contact of the knife-edge pivot coincides with the

vertical face of the quadrant tank. Thus, of the hydrostatic forces acting on the

immersed quadrant, only the horizontal thrust acting on the vertical face of the

tank will exert a counter-clockwise moment about the knife-edge axis. In

addition to the quadrant clamping screw the balance arm incorporates a balance

pan, an adjustable counterbalance and an indicator which shows when the arm

is horizontal. This is important as a horizontal arm coincides with the condition