GATE 2020: Fluid Mechanics Quiz 7 (App update required to attempt this test)

A container with two circular vertical tubes of diameter d1 = 39.5 mm and d2 = 12.7 mm is partially filled with mercury. The equilibrium level of the liquid is shown on the left diagram. A cylindrical object made from solid brass is placed in the larger tube so that it floats, as shown in right diagram. Object is D = 37.5 mm in diameter and H = 76.2 mm high. What will be the new equilibrium level, h of mercury with the brass cylinder in place?
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Water is coming out to the atmosphere from a converging channel with a velocity of 5 m/s as shown in the figure. At section A, a cylinder of 10 cm diameter containing a friction-less piston attached to a spring having spring constant 500 N/m is connected. The cross-section diameter of the channel at A and B is 2 m and 1 m respectively. Due to the flow the spring is compressed by an amount of

The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m³ flowing through a pipe. The acceleration due to gravity is 9.81 m/s². If the manometric fluid is water (density 1000 kg/m³) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is _____