GATE XE format:nat PYQs & Answers — Page 39

Questions 381–390 of 668. Imported answers require independent review unless marked reviewed.

Topic practice 668 questionsPage 39 of 67

Suppose, because of the doubling of atmospheric CO₂ concentration, an ocean water column receives an additional net energy input of 1 Wm⁻². If the entire water column of depth 1 km heats up uniformly, the water temperature will increase by 1 K in ____ years (round off to the nearest integer).

Assume all the additional heat added is retained and not lost. Take density of seawater = 1000 kg m⁻³; specific heat capacity of seawater = 4200 J kg⁻¹ K⁻¹.

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Consider a layer of atmosphere between 5 and 6 km height. The downwelling longwave radiation at 5 and 6 km is 240 and 230 Wm⁻², respectively. The upwelling longwave radiation at these heights is 260 and 240 Wm⁻², respectively. The longwave heating rate in this layer is ____ K per day. (Round off to one decimal place.)

Take the average density of air in this layer to be 0.5 kg m⁻³; Specific heat capacity of air at constant pressure = 1000 J kg⁻¹ K⁻¹.

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A spherical asteroid, revolving around the sun in a circular orbit, is in radiative balance. Suddenly, the asteroid enters the shadow of a planet and solar radiation is cut off. Assuming that the asteroid emits as a blackbody in the longwave regime, the time taken to reduce the average temperature of the asteroid by 0.5 K is ____ seconds (round off to the nearest integer). Ignore the temporal change in radiation emitted by the asteroid during this cooling period. The physical properties of the asteroid are: diameter = 2 m, density = 3000 kg m⁻³, specific heat = 200 J kg⁻¹ K⁻¹ and albedo = 0.8 in shortwave radiation. Take the solar constant = 500 W m⁻², Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

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Let

be a continuous function on the real line such that for any

. Then

is _____.

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The number of points at which the function

has local minima is _____.

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Players

and

take turns to throw a fair dice with six faces. If

is the first player to throw, then the probability of

being the first one to get a six is ____ (round off to two decimal places).

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A liquid flow through a horizontal smooth pipe of diameter 5 cm and discharges into a collection tank of dimension 50 cm x 50 cm x 50 cm. Time taken for a 10 cm rise of liquid level in the collection tank is 40 s.

The flow velocity in the pipe is ------ m/s (rounded off to two decimal places).

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The potential function for a two dimensional incompressible flow field is given as:

Magnitude of the velocity vector at point (2,1) is ________ m/s

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A hydroelectric power plant takes in 30 m

/s of water through its turbine and discharges it to the atmosphere with

m/s. The total head loss in the turbine and penstock system is 20 m. (Assume turbulent flow with kinetic energy correction factor as 1.1. Density of water is 1000 kg/m

and acceleration due to gravity, g is 10 m/s

The net head available to the turbine for power generation is --------------- m.

(rounded off to one decimal place).

Diagram for Engineering Sciences question 15

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Water flows at an average velocity,

of 10 m/s through a horizontal smooth tube of diameter,

5 cm. The friction factor,

is 0.02. Head loss is obtained using Darcy-Weisbach relation

. The fluid pressure,

measured at various stations are reported in the table below. The length of the pipe,

between station 0 and station 6 is 6 m.

Station	0	1	2	3	4	5	6
, kPa	304	273	255	240	226	213	-

If acceleration due to gravity, g = 10 m/s

and density of water =1000 kg/m

, then the fluid pressure at station 6 is ______ kPa (rounded off to one decimal place)

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GATE XE format:nat PYQs

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Question 15

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