Steam enters a circular pipe at 1600 kPa ....?

The volume entering the pipe and exiting the pipe must be the same.

So in one second,

V1(entering pipe) = Pi X (15/200)^2 X 10 and

V2(leaving pipe) = Pi X (D/2)^2 X 32

Equating, V1 = V2

After cancelling Pi on both sides of equation,

so 0.05625 = 8D^2

working, D = 0.08385m = 8.39 cm.

Using P1/T1 = P2/T2

where P1 = 1600kPa, T1 = 673K and P2 = 1000kPa

then 1600 / 673 = 1000 / T2

so T2 = 420.625K

which is 147.625 degree C = 148 degree C.

Hope it helps.

use eqn of continuity

A1v1=A2v2

get A2

then bernoulli's principle