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?
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The velocity field of a certain two-dimensional flow is given by
V(π₯, π¦) = π(π₯πΜ β π¦πΜ)
where π = 2 s-1. The coordinates π₯ and π¦ 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)
Consider a unidirectional fluid flow with the velocity field given by
V(π₯, π¦, π§, π‘) = π’(π₯, π‘) πΜ
where π’(0,π‘) = 1. If the spatially homogeneous density field varies with time π‘ as
π(π‘) = 1 + 0.2πβπ‘
the value of π’(2, 1) is ______________. (Rounded off to two decimal places) Assume all quantities to be dimensionless.
An explosion at time t = 0 releases energy πΈ at the origin in a space filled with a gas of density Ο. 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 π = π π‘π πΈ π ππ, where k is a dimensionless constant. The value of exponent a is ___________.
(Rounded off to one decimal place)