For a valve with a head loss coefficient K observed to be proportional to 1/(opening)^2. If the opening is halved, by what factor does K increase?

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Multiple Choice

For a valve with a head loss coefficient K observed to be proportional to 1/(opening)^2. If the opening is halved, by what factor does K increase?

Explanation:
The head loss coefficient scales with the inverse square of the opening. If the opening is halved, the new K is proportional to (1/(0.5 opening)^2) = 4 times the original. In other words, K increases by a factor of four. This happens because reducing the opening increases the flow velocity through the valve, and head losses grow with the square of velocity, leading to a fourfold increase in K.

The head loss coefficient scales with the inverse square of the opening. If the opening is halved, the new K is proportional to (1/(0.5 opening)^2) = 4 times the original. In other words, K increases by a factor of four. This happens because reducing the opening increases the flow velocity through the valve, and head losses grow with the square of velocity, leading to a fourfold increase in K.

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