# Venturimeter

### Venturimeter

#### Venturimeter terbuka

Venturimeter terbuka digunakan untuk mengukur kelajuan aliran zat cair.

$$A_1 > A_2 \rightarrow v_1 < v_2 \rightarrow P_1 > P_2$$

Penurunan Rumus

$$P_1 + \rho \: g \: h_1 + \frac{1}{2} \: \rho \: v_1^2 = P_2 + \rho \: g \: h_2 + \frac{1}{2} \: \rho \: v_2^2$$

Titik (1) dan (2) sejajar, maka $$h_1 = h_2$$

$$P_1 + \cancel {\rho \: g \: h_1} + \frac{1}{2} \: \rho \: v_1^2 = P_2 + \cancel {\rho \: g \: h_2} + \frac{1}{2} \: \rho \: v_2^2$$

$$P_1 + \frac{1}{2} \: \rho \: v_1^2 = P_2 + \frac{1}{2} \: \rho \: v_2^2$$

$$P_1 - P_2 = \frac{1}{2} \: \rho \: v_2^2 - \frac{1}{2} \: \rho \: v_1^2$$

$$\Delta P = \frac{1}{2} \: \rho \: (v_2^2 - v_1^2)$$

Tekanan pada pipa adalah tekanan hidrostatis $$P = \rho \: g \: h$$

$$\rho \: g \: \Delta h = \frac{1}{2} \: \rho \: (v_2^2 - v_1^2)$$

$$\cancel {\rho} \: g \: \Delta h = \frac{1}{2} \: \cancel {\rho} \: (v_2^2 - v_1^2)$$

$$2 \: g \: \Delta h = (v_2^2 - v_1^2)$$

Persamaan kontinuitas $$A_1 \: v_1 = A_2 \: v_2 \rightarrow v_2 = \dfrac {A_1}{A_2} \: v_1$$

$$2 \: g \: \Delta h = \left[\left(\dfrac {A_1}{A_2} \:.\: v_1\right)^2 - v_1^2\right]$$

$$2 \: g \: \Delta h = \left[\left(\dfrac {A_1}{A_2}\right)^2 - 1\right] \:.\: v_1^2$$

$$v_1^2 = \dfrac{2 \: g \: \Delta h}{\left[\left(\dfrac {A_1}{A_2}\right)^2 - 1\right]}$$

$$v_1 = \sqrt {\dfrac{2 \: g \: \Delta h}{\left[\left(\dfrac {A_1}{A_2}\right)^2 - 1\right]}}$$

#### Venturimeter tertutup

Venturimeter tertutup digunakan untuk mengukur kelajuan aliran air.

$$A_1 > A_2 \rightarrow v_1 < v_2 \rightarrow P_1 > P_2$$

Penurunan Rumus

$$P_1 + \rho \: g \: h_1 + \frac{1}{2} \: \rho \: v_1^2 = P_2 + \rho \: g \: h_2 + \frac{1}{2} \: \rho \: v_2^2$$

Titik (1) dan (2) sejajar, maka $$h_1 = h_2$$

$$P_1 + \cancel {\rho \: g \: h_1} + \frac{1}{2} \: \rho \: v_1^2 = P_2 + \cancel {\rho \: g \: h_2} + \frac{1}{2} \: \rho \: v_2^2$$

$$P_1 + \frac{1}{2} \: \rho \: v_1^2 = P_2 + \frac{1}{2} \: \rho \: v_2^2$$

$$P_1 - P_2 = \frac{1}{2} \: \rho \: v_2^2 - \frac{1}{2} \: \rho \: v_1^2$$

$$\rho \: g \: (-\Delta h) - \rho' \: g \: (-\Delta h) = \frac{1}{2} \: \rho \: (v_2^2 - v_1^2)$$

$$g \: \Delta h \: (\rho' - \rho) = \frac{1}{2} \: \rho \: (v_2^2 - v_1^2)$$

$$\dfrac {2 \: g \: \Delta h \: (\rho' - \rho)}{\rho} = (v_2^2 - v_1^2)$$

Persamaan kontinuitas $$A_1 \: v_1 = A_2 \: v_2 \rightarrow v_2 = \dfrac {A_1}{A_2} \: v_1$$

$$\dfrac {2 \: g \: \Delta h \: (\rho' - \rho)}{\rho} = \left[\left(\dfrac {A_1}{A_2} \:.\: v_1\right)^2 - v_1^2\right]$$

$$\dfrac {2 \: g \: \Delta h \: (\rho' - \rho)}{\rho} = \left[\left(\dfrac {A_1}{A_2}\right)^2 - 1\right] \:.\: v_1^2$$

$$v_1^2 = \dfrac{2 \: g \: \Delta h \: (\rho' - \rho)}{\rho \: \left[\left(\dfrac {A_1}{A_2}\right)^2 - 1\right]}$$

$$v_1 = \sqrt {\dfrac{2 \: g \: \Delta h \: (\rho' - \rho)}{\rho \: \left[\left(\dfrac {A_1}{A_2}\right)^2 - 1\right]}}$$