As the summer intern for a company that manufactures nozzles for garden hoses, you are working...

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).

Solutions

Expert Solution

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

genius_generous answered 1 year ago

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