List of top Fluid Mechanics and Thermal Sciences Questions asked in GATE Metallurgy

A ram in the form of a rectangular body of size l=9m and b=2m is suspended by two parallel ropes of lengths 7m. Assume the center-of-mass of the body is at its geometric center and g = 9.81m/s². For striking the object P with a horizontal velocity of 5m/s, what is the angle θ with the vertical from which the ram should be released from rest?

A heat pump (H.P.) is driven by the work output of a heat engine (H.E.) as shown in the figure. The heat engine extracts 150 kJ of heat from the source at 1000 K. The heat pump absorbs heat from the ambient at 280 K and delivers heat to the room which is maintained at 300 K. Considering the combined system to be ideal, the total amount of heat delivered to the room together by the heat engine and heat pump is _____kJ (answer in integer).

A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance L travelled by the liquid meniscus inside the capillary in time t is given by
L = ky^aR^bµ√t,
where γ is the surface tension, R is the inner radius of the capillary, and µ is the dynamic viscosity of the liquid. If k is a dimensionless constant, then the exponent α is ___ (rounded off to 1 decimal place).

Consider a hemispherical furnace of diameter D=6m with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of 300K and 1200K, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is _____kW (rounded off to the nearest integer).
Use Stefan-Boltzmann constant = 5.67×10-8 W/(m²K⁴)

A plane, solid slab of thickness L, shown in the figure, has thermal conductivity k that varies with the spatial coordinate x as k = A + Bx, where A and B are positive constants (A > 0, B > 0). The slab walls are maintained at fixed temperatures of T(x = 0) = 0 and T(x = L) = T₀ > 0. The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?

A piston-cylinder arrangement shown in the figure has a stop located 2m above the base. The cylinder initially contains air at 140kPa and 350°C and the piston is resting in equilibrium at a position which is 1m above the stops. The system is now cooled to the ambient temperature of 25°C. Consider air to be an ideal gas with a value of gas constant R = 0.287kJ/(kg.K).
The absolute value of specific work done during the process is _____kJ/kg (rounded off to 1 decimal place)

Consider an air-standard Brayton cycle with adiabatic compressor and turbine, and a regenerator, as shown in the figure. Air enters the compressor at 100 kPa and 300 K and exits the compressor at 600 kPa and 550 K. The air exits the combustion chamber at 1250 K and exits the adiabatic turbine at 100 kPa and 800 K. The exhaust air from the turbine is used to preheat the air in the regenerator. The exhaust air exits the regenerator (state 6) at 600 K. There is no pressure drop across the regenerator and the combustion chamber. Also, there is no heat loss from the regenerator to the surroundings. The ratio of specific heats at constant pressure and volume is \(\frac{C_p}{C_v} = 1.4\). The thermal efficiency of the cycle is _____% (answer in integer).

Consider a slab of 20mm thickness. There is a uniform heat generation of \(\dot{q}\) = 100MW/m³ inside the slab. The left and right faces of the slab are maintained at 150°C and 110°C, respectively. The plate has a constant thermal conductivity of 200W/(m.K). Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at (answer in integer).

A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1kg/s with an inlet temperature of 30°C. The steam in the condenser shell condenses at the rate of 430kg/s at a temperature of 50°C. If the heat of vaporization is 2.326MJ/kg and specific heat of water is 4kJ/(kg.K), the effectiveness of the heat exchanger is _____ (rounded off to 3 decimal places).

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W, N, and S with point J have an equal length L. The pipe connecting points J and E has a length 10L. The pressures at the ends N, E, and S are equal. The flow rate in the pipe connecting W and J is Q. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements:
I: The flow rate in pipe connecting J and E is \(\frac{Q}{21}\).
II: The pressure difference between J and N is equal to the pressure difference between J and E.
Which one of the following options is CORRECT?

Steady, compressible flow of air takes place through an adiabatic converging- diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?

A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is

Which one of the following statements regarding a Rankine cycle is FALSE?

The velocity field of a two-dimensional, incompressible flow is given by
\(\overrightarrow{V} = 2 sinh\ x\ \vec{i} + v(x, y)\vec{j}\)
where \(\vec{i}\ \text{and}\ \vec{j}\) denote the unit vectors in x and y directions, respectively. If v(x, 0) = cosh x, then v(0, -1) is

Consider incompressible laminar flow over a flat plate with freestream velocity of u_∞. The Nusselt number corresponding to this flow velocity is Nu₁. If the freestream velocity is doubled, the Nusselt number changes to Nu₂. Choose the correct option for Nu₂/Nu₁.

Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements, T is the temperature of the fluid, T_w is the wall temperature and T_m is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?

Tmin=300 K,Tmax=1200K,Q=1200 KJ.Find work done.

A linear spring mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitude of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping in (N.s/m) is