## Chapter 1

## 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

## Step-by-Step

## 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).