her0'es a question on fluid mechanics:

i need help in showing how to arrive at the expressions

3 a)

Air obeying Boyles law [imath] p=k \rho [/imath] is in motin in a uniform tube of small

cross-sectional area. show that if [imath] \rho [/imath] is the density and u is the velocity

at a distance x from a fixed point a; and t is time , this is true:

$\displaystyle \frac{ \partial^2 \rho}{\partial t^2} = \frac {\partial^2 \left[ (u^2 + k) \rho \right] }{\partial x^2} $

and here's another , any clues on how to start?

3 b. A steam is rushing from a boiler throught a conical pipe, the diameters of the ends a

being D and d . if v and u are the corresponding velocities of the steam an if the motion is

supposed to be that of divergence from the vortex of the cone prove that

$\displaystyle \frac{u}{v} = \frac {D^2} {d^2} e^{\frac{u^2-v^2}{2k} }$

where k is the pressure divide by the density and its a constant ie [imath] k= \frac{p}{\rho} [/imath]

note its getting in at one end with a velocity [imath] v [/imath] and density [imath] \rho_1 [/imath]

and out the other side with [imath] u [/imath] and [imath] \rho_2 [/imath]

i had posted the here mathbin.net/37252 but i managed the others this is whats troubling me