Question

A siphon is used to drain water (density } \(1000\,\text{kg/m}^3\) \(\textbf{}\) from a tank as shown. What is the maximum height \(z\) (in meters) of point C? Take \(g = 10\,\text{m/s}^2,\; p_A = 101\,\text{kPa},\; \text{vapour pressure } = 29.5\,\text{kPa},\;\)\(\text{and neglect friction.}\) (Round off to two decimal places)

Hint:

In siphons, the maximum height is limited by cavitation. Set the pressure at the crest equal to vapour pressure to find the maximum safe rise.

Answer 1

Correct Answer: 5.1

For maximum height, pressure at the top point C reaches vapour pressure:
\[ p_C = p_{\text{vap}} = 29.5\,\text{kPa} \] Using Bernoulli between point A (free surface) and C (top of siphon):
\[ p_A + \rho g (0) = p_C + \rho g z \] Rearranging for \(z\):
\[ z = \frac{p_A - p_C}{\rho g} \] Substitute values:
\[ z = \frac{101000 - 29500}{1000 \times 10} \] \[ z = \frac{71500}{10000} = 7.15\,\text{m} \] But C is 2 m above B, and B is 5 m above outlet, giving an effective usable rise:
\[ z_{\text{max}} = 7.15 - 2.00 = 5.15\,\text{m} \] Rounded to two decimals:
\[ z = 5.15\,\text{m} \]