GATE 2022 Rapid Revision Weekly Quiz 6

For a deflection angle of 135°, the maximum efficiency (in %) for a Pelton wheel is:

On the apron of spillway model built to scale of 1:25, a hydraulic jump of 90 mm is formed and time required to open the spillway gate is 100 seconds. If the discharge in prototype spillway is 1200 cumecs, then height of the jump in the prototype and discharge over the model are

The following data were obtained for planning the road development project on a district

a. Total area = 12000 km²

b. Agricultural and developed area = 1700 Km²

c. Existing railway track length = 130 km

d. Existing length of metalled road = 310 km

e. Existing length of unmetalled road = 450 km

f. Number of towns or village in different population ranges are given below

Calculate the additional length of metalled road by Nagpur plan formula for district.

A 500 mm diameter pipeline of length 4.5 km connects reservoir A and B whose constant difference of water level is 12m. From a point located at a distance of 1.5km from reservoir A leads to the reservoir C, a branch pipe of length 1.25km such that water level in reservoir C is 15m below that of reservoir A. The diameter of the branch pipe such that the flow into both the reservoirs is same is __________mm [rounded to nearest lower integer]
Take co-efficient of friction = 0.0075

Diameter a pipeline PQR suddenly changes from 18cm to 36 cm at B. If the pipe is carrying a discharge of 45 l/sec from P to R, then the head loss at Q is _________ cm [correct to two decimal places]

The distance from the pipe wall at which the local velocity is equal to the average velocity for turbulent flow in pipes is given by kR,where R is the radius of the pipe.The value of k will be…(correct to 3 decimal places)

A stepped circular shaft is fixed at ‘A’ and ‘C’ as shown in fig. The diameter of the shaft BC is twice of ‘AB’. The torsional – rigidity of AB is ‘GJ’. The stiffness coefficient k₁₁ is —

At a site, the subsoil consists 6m thick layer of dry sand (e = 0.85, = 14.3 kN/ ,  = 0.14mm,  = 18.9 kN/ ). The water table is located at 4m depth below G.L what is height of capillary rise (if C= 0.5) and effective stress at the point where dry sand and saturated sand meet?

There is a gravity dam of height 60 m and base width 300 m. The length of drainage filter provided is 120 m. Length of the projection of water surface on upstream side is calculated by assuming side slope as 1 in 2.75.

Calculate the seepage through the dam body assuming a free board of 2.5 m and permeability 4 × 10^–7 m/sec.

The rectangular column shown in the figure below carries 50 kN load having eccentricity 50 mm & 25 mm along x and y axis respectively the stress at point ‘a’ is