The three-fluid manometer illustrated in Figure P4.11 is used to measure a very small pressure difference $\left(P_{1}-P_{2}\right)$. The cross-sectional area of each of the reservoirs is $A$ and that of the manometer legs is $a$. The three fluids have densities $ho_{a}, ho_{b}$, and $ho_{c}$, and the

FIGURE P4.11 Three fluid manometer. difference in elevation of the interfaces in the reservoir is $x$. Derive the equation that relates the manometer reading $h$ to the pressure difference $\left(P_{1}-P_{2}\right)$. How would the relation be simplified if $A \gg a$ ?

Transcribed Image Text:

Fluid a Fluid c 1 x 2 h Fluid b