## Q. 1.SP.1

Bernoulli’s equation for the flow of an ideal fluid, which is discussed in Chap. 5 , can be written

$\frac{p}{\gamma}+z+\frac{V^2}{2 g}=\text { constant }$              ( 5.7)

where $p=$ pressure, $\gamma=$ specific weight, $z=$ elevation, $V=$ mean flow velocity, and $g=$ acceleration of gravity. Demonstrate that this equation is dimensionally homogeneous, i.e., that all terms have the same dimensions

## Verified Solution

Term 1:           Dimensions of $\frac{p}{\gamma}=\frac{F / L^2}{F / L^3}=L$

Term 2:           Dimensions of $z=L$

Term 3:           Dimensions of $\frac{V^2}{2 g}=\frac{(L / T)^2}{L / T^2}=L$

So all the terms have the same dimensions, $L$, which must also be the dimensions of the constant at the right-hand side of Eq. (5.7).