When the energy balance on the fluid in a stream tube is written in the following form, it is known as the Bernoulli equation:

\[\frac{P_{2}-P_{1}}{ho}+g\left(z_{2}-z_{1}\right)+\frac{\alpha}{2}\left(V_{2}^{2}-V_{1}^{2}\right)+e_{f}+w=0,\]

where

$w$ is the work done on a unit mass of fluid

$e_{f}$ is the energy per unit mass dissipated by friction in the fluid, including all thermal energy effects due to heat transfer or internal generation

$\alpha$ is equal to either 1 or 2 for turbulent or laminar flow, respectively

If $P_{1}=25 \mathrm{psig}, P_{2}=10 \mathrm{psig}, z_{1}=5 \mathrm{~m}, z_{2}=8 \mathrm{~m}, V_{1}=20 \mathrm{ft} / \mathrm{s}, V_{2}=5 \mathrm{ft} / \mathrm{s}, ho=62.4 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}, \alpha=1$, and $w=0$, calculate the value of $e_{f}$ in each of the following systems of units:

(a) $\mathrm{SI}$

(b) mks engineering (e.g., metric engineering)

(c) English engineering

(d) English scientific (with $\mathrm{M}$ as a fundamental dimension)

(e) English thermal units (e.g., Btu)

(f) Metric thermal units (e.g., calories)