Topic: Fluid Mechanics
The maximum height of a siphon for a fluid of specific gravity $\rho$ under atmospheric conditions is
- A. $\rho/10$ meters
- B. $\frac{10(1+\rho)}{\rho}meters$
- C. $10/(1-\rho)$ meters
- D. $10/\rho$ meters
Answer: D. $10/\rho$ meters
Explanation: Assuming initially the tank has water in it ($V_{1}=0$, $Z_{1}=0$). Applying Bernoulli's equation: $\frac{P_{0}}{\rho g}+\frac{0^{2}}{2g}+0=\frac{P_{2}}{\rho g}+\frac{V_{2}^{2}}{2g}+Z_{2}$. For maximum height, pressure at the highest point is zero and velocity is assumed zero. So $P_{0}=P_{atm}$. $\frac{P_{0}}{\rho g}=Z_{2}=y$. For water, $y=\frac{100000}{1000\times10}=10~m$. For another fluid, $\rho_{f}gh=\rho_{w}\times g\times y \implies h=\frac{10}{(\rho_{f}/\rho_{w})} = \frac{10}{\rho}$ m where $\rho$ is specific gravity.