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

AI Thread Summary
The discussion focuses on calculating the pressure and speed of water in a fire hose tip based on given parameters. The initial gauge pressure in the hose is 3.0 x 10^5 Nm-2, with a flow speed of 4.0 m/s. Using the continuity equation and Bernoulli's principle, the volumetric flow rate is determined to be 0.00916 m3/s, leading to a calculated speed at the hose tip of 18.67 m/s. The pressure at the tip is computed to be approximately 133,716 N/m^2 after correcting for arithmetic errors. The accuracy of these calculations is questioned in relation to tutorial answers.
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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.
 
Physics news on Phys.org
You have to square the 18.67. Check your arithmetic. I get 133,716 N/m^2.

AM
 
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