A. Venturimeter terbuka

Venturimeter terbuka digunakan untuk mengukur kelajuan aliran zat cair.

 

 

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

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 $h_1=h_2$

$P_1+\cancel{\rho g{h}_1}+\frac{1}{2}\rho v_1^2=P_2+\cancel{\rho g{h}_2}+\frac{1}{2}\rho v_2^2$

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

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

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

 

Tekanan pada pipa adalah tekanan hidrostatis $P=\rho gh$

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

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

$2g\mathrm{\Delta }h=(v_2^2-v_1^2)$

 

Persamaan kontinuitas $A_1{v}_1=A_2{v}_2\to v_2={\displaystyle \frac{A_1}{A_2}}{v}_1$

$2g\mathrm{\Delta }h=[{({\displaystyle \frac{A_1}{A_2}}.v_1)}^2-v_1^2]$

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

 

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

 

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

B. Venturimeter tertutup

Venturimeter tertutup digunakan untuk mengukur kelajuan aliran air.

 

 

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

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 $h_1=h_2$

$P_1+\cancel{\rho g{h}_1}+\frac{1}{2}\rho v_1^2=P_2+\cancel{\rho g{h}_2}+\frac{1}{2}\rho v_2^2$

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

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

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

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

${\displaystyle \frac{2g\mathrm{\Delta }h({\rho }^{\prime }-\rho )}{\rho }}=(v_2^2-v_1^2)$

 

Persamaan kontinuitas $A_1{v}_1=A_2{v}_2\to v_2={\displaystyle \frac{A_1}{A_2}}{v}_1$

${\displaystyle \frac{2g\mathrm{\Delta }h({\rho }^{\prime }-\rho )}{\rho }}=[{({\displaystyle \frac{A_1}{A_2}}.v_1)}^2-v_1^2]$

${\displaystyle \frac{2g\mathrm{\Delta }h({\rho }^{\prime }-\rho )}{\rho }}=[{\left({\displaystyle \frac{A_1}{A_2}}\right)}^2-1].v_1^2$

 

$v_1^2={\displaystyle \frac{2g\mathrm{\Delta }h({\rho }^{\prime }-\rho )}{\rho [{\left({\displaystyle \frac{A_1}{A_2}}\right)}^2-1]}}$

 

$v_1=\sqrt{{\displaystyle \frac{2g\mathrm{\Delta }h({\rho }^{\prime }-\rho )}{\rho [{\left({\displaystyle \frac{A_1}{A_2}}\right)}^2-1]}}}$

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 $v_1=0$

$P_1+\cancel{\rho g{h}_1}+0=P_2+\cancel{\rho g{h}_2}+\frac{1}{2}\rho v_2^2$

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

$\mathrm{\Delta }P=\frac{1}{2}\rho v_2^2$

${\rho }^{\prime }g\mathrm{\Delta }h=\frac{1}{2}\rho v_2^2$

$v_2^2={\displaystyle \frac{2{\rho }^{\prime }g\mathrm{\Delta }h}{\rho }}$

$v_1=\sqrt{{\displaystyle \frac{2{\rho }^{\prime }g\mathrm{\Delta }h}{\rho }}}$