Berdasarkan persamaan kontinuitas:
\begin{align*} A_1v_1 &= A_2v_2 \\ v_2 &= \frac{A_1}{A_2} \, v_1 \end{align*}
Menggunakan persamaan Bernoulli:
P_1 + \frac{1}{2}\rho_u v_1^2 + \rho_u gh_1 = P_2 + \frac{1}{2}\rho_u v_2^2 + \rho_u gh_2
Ketinggian titik 1 dan 2 sama h_1 = h_2)
P_1 + \frac{1}{2}\rho_u v_1^2 = P_2 + \frac{1}{2}\rho_u v_2^2
Substitusi v_2
\begin{align*} P_1 + \frac{1}{2}\rho_u v_1^2 &= P_2 + \frac{1}{2}\rho_u \left(\frac{A_1}{A_2}\right)^2 v_1^2 \\ P_1 - P_2 &= \frac{1}{2}\rho_u v_1^2 \left[ \left(\frac{A_1}{A_2}\right)^2 - 1 \right] \end{align*}
Perbedaan tekanan antara titik 1 dan 2 (P_1 - P_2) adalah sebesar perbedaan tekanan hidrostatik udara dengan tekanan hidrostatik fluida (\rho_f g \Delta h - \rho_u g \Delta h)
\begin{align*} \rho_f g \Delta h - \rho_u g \Delta h &= \frac{1}{2}\rho_u v_1^2 \left[ \left(\frac{A_1}{A_2}\right)^2 - 1 \right] \\ (\rho_f - \rho_u) g \Delta h &= \frac{1}{2}\rho_u v_1^2 \left[ \left(\frac{A_1}{A_2}\right)^2 - 1 \right] \\ v_1 &= \sqrt{\frac{2g\Delta h (\rho_f - \rho_u)}{\rho_u \left[ \left( \frac{A_1}{A_2} \right)^2 -1 \right]}} \end{align*}
\begin{align*} A_1v_1 &= A_2v_2 \\ v_2 &= \frac{A_1}{A_2} \, v_1 \end{align*}
Menggunakan persamaan Bernoulli:
P_1 + \frac{1}{2}\rho_u v_1^2 + \rho_u gh_1 = P_2 + \frac{1}{2}\rho_u v_2^2 + \rho_u gh_2
Ketinggian titik 1 dan 2 sama h_1 = h_2)
P_1 + \frac{1}{2}\rho_u v_1^2 = P_2 + \frac{1}{2}\rho_u v_2^2
Substitusi v_2
\begin{align*} P_1 + \frac{1}{2}\rho_u v_1^2 &= P_2 + \frac{1}{2}\rho_u \left(\frac{A_1}{A_2}\right)^2 v_1^2 \\ P_1 - P_2 &= \frac{1}{2}\rho_u v_1^2 \left[ \left(\frac{A_1}{A_2}\right)^2 - 1 \right] \end{align*}
Perbedaan tekanan antara titik 1 dan 2 (P_1 - P_2) adalah sebesar perbedaan tekanan hidrostatik udara dengan tekanan hidrostatik fluida (\rho_f g \Delta h - \rho_u g \Delta h)
\begin{align*} \rho_f g \Delta h - \rho_u g \Delta h &= \frac{1}{2}\rho_u v_1^2 \left[ \left(\frac{A_1}{A_2}\right)^2 - 1 \right] \\ (\rho_f - \rho_u) g \Delta h &= \frac{1}{2}\rho_u v_1^2 \left[ \left(\frac{A_1}{A_2}\right)^2 - 1 \right] \\ v_1 &= \sqrt{\frac{2g\Delta h (\rho_f - \rho_u)}{\rho_u \left[ \left( \frac{A_1}{A_2} \right)^2 -1 \right]}} \end{align*}