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The volume of a liquied following out pe...

The volume of a liquied following out per second of a pipe of length I and radius r is written by a student as `upsilon =(pi)/(8)(Pr^4)/(etaI)` where P is the pressure difference between the two ends of the pipe and `eta` is coefficient of viscosity of the liquid having dimensioal formula `ML^(-1)T^(-1).` Check whether the equation is dimensionally correct.

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To check if the equation \( \nu = \frac{\pi}{8} \frac{P r^4}{\eta L} \) is dimensionally correct, we will analyze both sides of the equation to ensure they have the same dimensions. ### Step 1: Determine the dimensions of the left-hand side (LHS) The left-hand side \( \nu \) represents the volume of liquid flowing out per second. - The dimension of volume is given by \( L^3 \). - Since it is a flow rate (volume per unit time), we divide by time \( T \). ...
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