A. Venturimeter terbuka

Venturimeter terbuka digunakan untuk mengukur kelajuan aliran zat cair.

 

 

\(A_1 > A_2 \rightarrow v_1 < v_2 \rightarrow P_1 > P_2\)

Permukaan cairan pada pipa (1) lebih tinggi daripada permukaan cairan pada pipa (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 \(A_1 \: v_1 = A_2 \: v_2 \rightarrow v_2 = \dfrac {A_1}{A_2} \: v_1\)

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

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

 

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

 

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

B. Venturimeter tertutup

Venturimeter tertutup digunakan untuk mengukur kelajuan aliran air.

 

 

\(A_1 > A_2 \rightarrow v_1 < v_2 \rightarrow P_1 > P_2\)

Maka permukaan fluida pada pipa (1) lebih rendah daripada permukaan fluida pada pipa (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 \(A_1 \: v_1 = A_2 \: v_2 \rightarrow v_2 = \dfrac {A_1}{A_2} \: v_1\)

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

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

 

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

 

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

C. Tabung Pitot

tabung pitot digunakan untuk mengukur kelajuan aliran gas

 

 

Pada tabung pitot, mulut pipa (1) diarahkan tegak lurus terhadap arah aliran gas (menjauhi pembaca), sehingga \(v_1 = 0\)

 

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 \(h_1 = h_2\) dan \(v_1 = 0\)

\(P_1 + \cancel {\rho \: g \: h_1} + 0 = P_2 + \cancel {\rho \: g \: h_2} + \frac{1}{2} \: \rho \: v_2^2\)

\(P_1 - P_2 = P_2 + \frac{1}{2} \: \rho \: v_2^2\)

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

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

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

\(v_1 = \sqrt {\dfrac{2 \rho' \: g \: \Delta h}{\rho}}\)