The volume V of water passing any point of a uniform tube during t seconds is related to the cross-sectional area A of the tube and velocity u of water by the relation $$V \propto A^{\alpha} u^ {\beta} t^ {\gamma}$$

Which one of the following will be true ?

Question

The volume V of water passing any point of a uniform tube during t seconds is related to the cross-sectional area A of the tube and velocity u of water by the relation  $$V \propto A^{\alpha} u^ {\beta} t^ {\gamma}$$

Which one of the following will be true ?

unklerhaukus · Answer

$$[\textbf L]^3\propto [\mathbf L^2]^\alpha\cdot\frac{[\mathbf L]^\beta}{[\mathbf T]^\beta}\cdot[\mathbf T]^\gamma$$

mathslover · Answer

Yep Unkle. I then continued the process getting : $$2\alpha + \beta = 3 $$ and $$-\beta + \gamma = 0 $$

mathslover · Answer

I think the situation or condition is satisfied at $\alpha = \beta = \gamma$ but if we talk about the general equation or form, it is : $\alpha \ne \beta = \gamma$

mathslover · Answer

$\large{\alpha \ne \beta =  \gamma}$ is correct for each and every real value. But $\alpha = \beta = \gamma$ satisfies only if all are equal to 1.

unklerhaukus · Answer

why do you say $α≠β$?

mathslover · Answer

$\alpha \ne \beta$ because $\alpha = \cfrac{3-\beta}{2}$ .

unklerhaukus · Answer

i dont understand that bit.

mathslover · Answer

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