In: Physics
As the summer intern for a company that manufactures nozzles for garden hoses, you are working on a project involving adjustable hose nozzles. Your design calls for a rotating head that has a number of cylindrical plugs that can be inserted into the hose opening. On a particular setting, the speed of the water passing around the plug is 7 times as large as the speed of the water in the hose. Determine the ratio of the plug radius (rplug) to the inside hose radius (rhose).
Radius of the hose = R1
Speed of flow of water in the hose = V1
Cross-sectional area of the hose = A1
A1 = R12
Radius of the cylindrical plug = R2
Speed of flow of water around the plug = V2
Cross-sectional area of the plug = A2
A2 = R22
The speed of water passing around the plug is 7 times as large as the speed of the water in the hose.
V2 = 7V1
When the water flows around the plug in the hose it will flow through an area between the hose and the plug that is (A1 - A2).
By continuity equation,
A1V1 = (A1 - A2)V2
R12V1 = (R12 - R22)(7V1)
R12 = 7(R12 - R22)
Ratio of the plug radius to the inside hose radius - 0.926