Consider a sphere moving through a viscous fluid completely submerged. The indicial method (Buckinham's Pi Theorem)...

 

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Consider a sphere moving through a viscous fluid completely submerged. The indicial method (Buckinham's Pi Theorem) is applied to study the relationship between the resistance to motion R, and the variables (the diameter of the sphere Ds, the density of the fluid p, viscosity and the mean velocity of the fluid v). As such, the dimension balance for these variables can be written as [R] = [D§]ª[v]¹[p][µ]ª. What are algebraic equations for the powers of the dimensions [M], [L], [T]? Hint: The resistance is drag force. (e.g., \emph[M]: a + 2 * b = 3) [M] [L] = [T]: = V R D Consider a sphere moving through a viscous fluid completely submerged. The indicial method (Buckinham's Pi Theorem) is applied to study the relationship between the resistance to motion R, and the variables (the diameter of the sphere Ds, the density of the fluid p, viscosity and the mean velocity of the fluid v). As such, the dimension balance for these variables can be written as [R] = [D§]ª[v]¹[p][µ]ª. What are algebraic equations for the powers of the dimensions [M], [L], [T]? Hint: The resistance is drag force. (e.g., \emph[M]: a + 2 * b = 3) [M] [L] = [T]: = V R D

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To determine the algebraic equations for the powers of the dimensions M L T in the resistance to ... View the full answer