Solving Water Nozzle Problem: Ratio of Plug Radius to Hose Radius

[curryman24]

THE PROBLEM
In an adjustable nozzle for a garden hose, a cylindrical plug is aligned along the axis of the hose and can be inserted into the hose opening. The purpose of the plug is to change the speed of the water leaving the hose. The speed of the water passing around the plug is to be 4 times greater than the speed of the water before it encounters the plug. Find the ratio of the plug radius to the inside hose radius.

The attempt at a solution:

I do know the equation of continuity and it is

(P1)(A1)(V1)= (P2)(A2)(V2)

and I used this to say that the pressure is going to be constant throughout the problem so it can be canceled.

So,
(A1)(V1)= (A2)(V2)
(πr1^2)(V1) = (πr2^2)(V2)
(r1^2)(V1) = (r2^2)(V2)
and V2= (4V1)
so (r1^2)(V1) = (r2^2)(4V1)
(r1^2) = (4r2^2)
(r2/r1) = 0.5

HOWEVER, this is wrong...please help.

 

[stewartcs]

You have found the ratio of the equivalent "hole" to the hose instead of the ratio of the "plug" to the hose.