A pump does not know what a building looks like. It knows one number: the total dynamic head it has to develop, in metres of the liquid it is moving. Everything the system asks of it gets converted into that one currency first, and only then added up.

$TDH = h_s + h_f + h_v$ — read aloud T D H equals h-s plus h-f plus h-v. $TDH$ is the head the pump must produce, in metres. $h_s$ is the static head: the height the liquid actually has to climb, plus any pressure that must still be there when it arrives. $h_f$ is the friction head, the metres the pipe, fittings and valves eat on the way — always positive, because friction only ever takes. $h_v$ is the velocity head, $h_v = \dfrac{v^{2}}{2g}$, the kinetic energy of the moving stream written as a height. The subscripts are a naming convention and nothing more: s for static, f for friction, v for velocity.

The trap is arithmetic dressed as physics. A spec sheet quotes the duty at the far end in kilopascals, and kilopascals cannot be added to metres. Convert first: $h = \dfrac{P}{\rho g}$ — h equals P over rho g — where $P$ is the pressure in pascals, $\rho$ (rho) is the liquid's density in kg/m³ and $g$ is 9.81 m/s². For water $\rho g$ is $9810\ \mathrm{N/m^3}$, which is 9.81 kN per cubic metre, so one metre of water is 9.81 kPa and 100 kPa is about 10.2 m. That single fact is the metric twin of the imperial trade's 2.31 feet per psi.

Units guide, they do not confess. A sum whose terms wear different units is not a sum, and the units will say so before the arithmetic does. But units that DO agree never prove the physics right — the check runs one way only.