List of top Mechanical Engineering Questions on Fluid Mechanics asked in GATE ME

Consider a unidirectional fluid flow with the velocity field given by
\(V(x, y, z, t) = u(x, t)\ \hat{i}\)
where \(u(0, t) = 1\). If the spatially homogeneous density field varies with time \(t\) as
\(\rho(t) = 1 + 0.2e^{-t}\), the value of \(u(2,1)\) is ................ (Rounded off to two decimal places).
Assume all quantities to be dimensionless.

An explosion at time \(t = 0\) releases energy \(E\) at the origin in a space filled with a gas of density \(\rho\). Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure.
Let \(R\) denote the radius of the front of the hemispherical blast wave. The radius \(R\) follows the relationship \(R = k t^a E^b \rho^c\), where \(k\) is a dimensionless constant. The value of exponent \(a\) is ................
(Rounded off to one decimal place)

The figure shows two fluids held by a hinged gate. The atmospheric pressure is \(P_a\) = 100 kPa. The moment per unit width about the base of the hinge is ............... kNm/m. (Rounded off to one decimal place)
Take the acceleration due to gravity to be g = 9.8 m/s².

The velocity field of a certain two-dimensional flow is given by
\(V(x, y) = k(x\hat{i} - y\hat{j})\)
where \(k = 2 \text{ s}^{-1}\). The coordinates x and y are in meters. Assume gravitational effects to be negligible.
If the density of the fluid is 1000 kg/m³ and the pressure at the origin is 100 kPa, the pressure at the location (2 m, 2 m) is ............... kPa.
(Answer in integer)

Air (density = 1.2 kg/m³, kinematic viscosity = 1.5×10⁻⁵ m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is \(\tau_w\). What is the wall shear stress at a location 30 mm from the leading edge?

Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:
\(P_1 = 100\) kPa, \(\rho_1 = 1.2\) kg/m³, \(u_1 = 400\) m/s
The duct cross-sectional area at Location 2 is given by \(A_2 = 2A_1\), where \(A_1\) denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity \(u_2\) and pressure \(P_2\) at Location 2 is TRUE?