The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure (P0) is increased while keeping the back pressure (Pback) unchanged, which of the following statements is/are true?

A solid spherical bead of lead (uniform density = 11000 kg/m³) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 10^-3 kg∙m^-1∙s^-1). The coefficient of drag is given by $\rm C_D = \frac{24}{Re} $, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as $\rm D = (C_D) (0.5 \rho V^2) \left( \frac{\pi d^2}{4} \right), $ where ρ is the density of the liquid. Neglect the buoyancy force. Using g = 10 m/s², the velocity V is __________ m/s.

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).