Question

The piston of the ball valve shown in Fig. 3.13 has an effective diameter of 10mm. The valve just closes when of the volume of the ball is submerged. Calcul te (552kN/I2) the pressure in kN/m2 of the mains supply Main 150mm diam supply 25 mm Pivot 250mm Fio. 3.13 A ball valve is arranged as in Question 4 but the distance from the centre of the ball to the pivot is 300mm and the diameter of the piston is 12-5mm. If the mains pressure is 690kN/m2, calculate what fraction of the ball is immersed. What would e the mains pressure if the valve closed when t of the ball was immersed? (0.4, 570kN/m2)

Answer 1

2 Buoyancy force on the ball is FB-P.water«V.xg Consider equilibrium of moments about pivot. Buoyancy force on the ball is: immersed volume=1×4m,3 radius of ball pivot ×V.xg B waterL let the immersed fraction be n xnxVxgx300 PxAp x25 (V-volume of the ball) L4π 150 x9.81 4.3393 F, =1000× × 2 1000 a(12.5 x25 4 1000 Consider equilibrium of moments about pivot. 3" 2000 x9.81x300 1000×n×5.2=21 16.89 n-0.40 pwot F x250-PxAnx25 P- pressure A-area of piston d use equation |2 4 piston 4.3393x250-Px10 1084.825-1.963495x10-3xP P=552,497 N/m2 P-552 kN/m2 41000X25 12.5x25 3 3 2000 1733.57-3.067x10-3P P-565,055 N/m2 P570 kN/m2