List of practice Questions

A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is 1.23 kg m\(^{-3}\) while the density of water is 1000 kg m\(^{-3}\). For the manometer reading of \( h = 30 \) mm of mercury, the speed of air in the wind tunnel is _________ m s\(^{-1}\) (rounded off to 1 decimal place). 

Consider a cylindrical furnace of 5 m diameter and 5 m length with bottom, top, and curved surfaces maintained at uniform temperatures of 800 K, 1500 K, and 500 K, respectively. The view factor between the bottom and top surfaces, \( F_{12} \), is 0.2. The magnitude of net radiation heat transfer rate between the bottom surface and the curved surface is _________ kW (rounded off to 1 decimal place).
[All surfaces of the furnace can be assumed as black.]
[The Stefan-Boltzmann constant, \( \sigma = 5.67 \times 10^{-8} \, {W m}^{-2} \, {K}^{-4} \)] 

The directional derivative of the function \( f \) given below at the point \( (1, 0) \) in the direction of \( \frac{1}{2} (\hat{i} + \sqrt{3} \hat{j}) \) is (rounded off to 1 decimal place). \[ f(x, y) = x^2 + xy^2 \]

If \( C \) is the unit circle in the complex plane with its center at the origin, then the value of \( n \) in the equation given below is (rounded off to 1 decimal place). \[ \int_C \frac{z^3}{(z^2 + 4)(z^2 - 4)} \, dz = 2 \pi i n \]

The system shown in the figure below consists of a cantilever beam (with flexural rigidity \( EI \) and negligible mass), a spring (with spring constant \( K \) and negligible mass) and a block of mass \( m \). Assuming a lumped parameter model for the system, the fundamental natural frequency (\( \omega_n \)) of the system is 

In relation to additive manufacturing, match the following:

Match the mold elements in the casting process with the most suitable function: 

Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are:

During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, 85% of the power is absorbed within a circle of radius 5 mm while 65% is absorbed within an inner concentric circle of radius 3 mm. The power density in the shaded area is _________ W mm^-2 (rounded off to 2 decimal places).

The values of a function \( f \) obtained for different values of \( x \) are shown in the table below.

Using Simpson’s one-third rule, approximate the integral \[ \int_0^1 f(x) \, dx \quad \text{(rounded off to 2 decimal places)}. \]

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?

\[ {Given: } F = 1000\,{N} \]

A rigid circular disc of radius \(r\) (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is \(\omega\) (in rad/ssuperscript{-1}). The velocities (in m/ssuperscript{-1}) at points 0 and A, respectively, are: