Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is _______ N.

A steady two-dimensional flow field is specified by the stream function

ψ = kx3y,

where x and y are in meters and the constant k = 1 m-2s-1. The magnitude of acceleration at a point (x, y) = (1 m, 1 m) is ________ m/s2 (round off to 2 decimal places).

A flat plate made of cast iron is exposed to a solar flux of 600 W/m² at an ambient temperature of 25 °C. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low-temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 × 10^-8 W/m²-K⁴. Neglect all other modes of heat transfer except radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ °C (round off to the nearest integer).

Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T_∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as 

$\rm \dot q = \cos \frac{2 \pi x}{L}$

The steady-state temperature at the mid-location of the rod is given as T_A. What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h?