Question

A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be :

• A. ${10}^{5}N/m$
• B. $2\times {10}^{5}N/m$
• C. Zero
• D. Infinity

Answer 1

The correct option is C Zero

Zero.
Both the points are located on the surface of liquid in the basins, which is open to the atmosphere. Therefore, the pressure at both the points will be equal to atmospheric pressure => pressure difference = 0.
NOTE:
Students may wonder how the pressure difference is zero, since the 2 points have a height difference of 10cm. When the the formula $P=P_0=\rho gh$ is applied, we get that the pressure difference should be non-zero.
It is important to note that the above formula is valid only in static fluids. Fluids in motion obey a formula called Bernoulli's principle. The water in the siphon is indeed not static and movies with a velocity such that it obeys Bernoulli's principle.