Question 1. A sector gate is provided on a spillway as shown in the figure. Assuming g = 10 m/s^{2}, the resultant force per meter length (expressed in kN/m) on the gate will be_______ . [2016 : 2 Marks, SetI]
Solution:
Question 2. A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8. Considering the density of water and acceleration due to gravity to be 1000 kg/m^{3} and 9.81 m/s^{2}, respectively, the hydrostatic force (in kN) exerted by the oil on the gate is _________ . [2015 : 2 Marks, SetII]
Solution:
Question 3. Three rigid buckets, shown as in the figures (1), (2) and (3), are of identical heights and base areas. Further, assume that each of these buckets have negligible mass and are full of water. The weight of water in these buckets are denoted as W_{1}, W_{2}, and W_{3} respectively. Also, let the force of water on the base of the bucket be denoted as F_{1}, F_{2}, and F_{3} respectively. The option giving an accurate description of the system physics is [2014 : 2 Marks, SetI]
(a) W_{2} = W_{1} = W_{3} and F_{2} > F_{1} > F_{3 }
(b) W_{2} > W_{1} > W_{3} and F_{2} > F_{1} > F_{3 }
(c) W_{2} = W_{1} = W_{3} and F_{1} = F_{2} = F_{3 }
(d) W_{2} > W_{1} > W_{3} and F_{1} = F_{2} = F_{3 }
Answer: (d)
Solution: Bucket → identical height → identical base area
=> w_{2}> w_{1}> w_{3 }
Force on the base in each case will be equal to =
Hence, F_{1} = P_{2} = F_{3}
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