Usaha dan Energi Pembahasan Soal 1

Debit air terjun 120m³/menit

Volume air = 120 m³ = 120.000 dm³ = 120.000 liter = 120.000 kg (1 liter air = 1 kg)

Waktu = 1 menit = 60 detik

Daya mesin (P output) = 100 kW = 100.000 W

Usaha dan perubahan energi potensial gravitasi

\begin{equation*}
\begin{split}
W_{\text{gravitasi}} & = -\Delta EP\\\\
W_{\text{gravitasi}} & = - (EP_2 - EP_1) \\\\
W_{\text{gravitasi}} & = - m \:.\: g \:.\: (h_2 - h_1) \\\\
W_{\text{gravitasi}} & = 120.000 \:.\: 10 \:.\: (0 - 40) \\\\
W_{\text{gravitasi}} & = 48.000.000 \text{ J}
\end{split}
\end{equation*}

Daya yang dihasilkan air terjun (P_input)

\begin{equation*}
\begin{split}
P_{\text{input}} & = \frac{W}{t} \\\\
P_{\text{input}} & = \frac{48.000.000}{60} \\\\
P_{\text{input}} & = 800.000 \text{ Watt}
\end{split}
\end{equation*}

Efisiensi turbin

\begin{equation*}
\begin{split}
\eta & = \frac{P_{\text{output}}}{P_{\text{input}}} \times 100 \% \\\\
\eta & = \frac{100.000}{800.000} \times 100 \% \\\\
\eta & = 12,5 \%
\end{split}
\end{equation*}