Question 23M.3.HL.TZ1.11
| Date | May 2023 | Marks available | [Maximum mark: 5] | Reference code | 23M.3.HL.TZ1.11 |
| Level | HL | Paper | 3 | Time zone | TZ1 |
| Command term | Calculate, Show, Suggest | Question number | 11 | Adapted from | N/A |
A siphon consists of a pipe AB of constant diameter that is used to empty a large tank of oil. The depth of the oil in the tank is 5.0 m and the outlet B of the pipe is 8.0 m below the free surface of the oil in the tank.
diagram not to scale
Show, using Bernoulli’s equation, that the speed of the oil as it leaves opening B is 12.5 m s−1.
[2]
«considering a streamline joining the surface of the oil to B»
«0 + 0 +» Patm = −gH + Patm + v2 ✓
v = = ✓
«= 12.53 m s−1»
Award 1 max for use of Torricelli theorem.
Do not accept a BCA, MP1 must be seen.
Suggest why the speed of the oil everywhere in the siphon is the same as that at B.
[1]
«by the equation of continuity v = const» because the diameter/area is constant ✓
Siphon. Most students applied the continuity equation well in b).
Calculate the maximum height h for which the siphon will work. The density of oil is 915 kg m−3 and the atmospheric pressure is 1.01 × 105 Pa.
[2]
setting pressure at highest point to zero gives «0 + 0 +» Patm = gh + 0 + v2 ✓
h = «» = 3.29 m ✓
Only the best students could identify the maximum height.