What Are the Pressure and Speed of Water in a Fire Hose Tip?

[mm874]

Homework Statement

The gauge pressure in a horizontal fire hose of diameter 5.4 cm is 3.0 x 105 Nm-2 and the speed of flow is 4.0 ms-1. The fire hose ends in a metal tip of diameter 2.5 cm. What are the pressure and the speed of the water in the tip?

Homework Equations

P+ρgh+0.5ρv^2=Constant
Volumetric Flow rate = A*v
Mass Flow Rate = ρ*Volumetric Flow rate

The Attempt at a Solution

Volumetric Flow rate = 0.00229*4 = 0.00916m3/s
Speed at end of hose = 0.00916/0.000491 = 18.67m/s

300000 + (0.5*1000*4^2) = P2 + (0.5*1000*18.67)
= 308000 = P2+174845

∴ P2 = 308000-17845 = 133155Pascals or 1.3 Bar

I am just checking this is right. As this is the answer I keep getting but the tutorial answers show something different.

 

[Andrew Mason]

You have to square the 18.67. Check your arithmetic. I get 133,716 N/m^2.

AM