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Why Rockets have a fixed diameter?

Is it possible to create a rocket with a variable blast diameter to achieve different levels of torque and power similar to a geared transmission?

I suppose the best analogy I have is the difference in power between a garden hose normally and when you plug it with your thumb, creating more pressure.

Would it be possible to have a rocket launch with maximum diameter, and slowly close up like a camera shutter to gain speed once in the air? Perhaps this shudder would be angled like a funnel to direct the blast easier. All the rockets I see have a fixed diameter and it just makes me curious.

(Asked Bharath)

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