| Date | May 2019 | Marks available | 1 | Reference code | 19M.3.HL.TZ1.10 |
| Level | Higher level | Paper | Paper 3 | Time zone | 1 |
| Command term | State | Question number | 10 | Adapted from | N/A |
Question
Gasoline of density 720 kg m–3 flows in a pipe of constant diameter.
State one condition that must be satisfied for the Bernoulli equation
ρv2 + ρgz + ρ = constant
to apply
Outline why the speed of the gasoline at X is the same as that at Y.
Calculate the difference in pressure between X and Y.
The diameter at Y is made smaller than that at X. Explain why the pressure difference between X and Y will increase.
Markscheme
flow must be laminar/steady/not turbulent ✔
fluid must be incompressible/have constant density ✔
fluid must be non viscous ✔
«continuity equation says» Av = constant «and the areas are the same» ✔
Bernoulli: « + 0 + Px = + pgH + Py » gives Px − Py = pgH ✔
Px − Py = 720 × 9.81 × 1.2 = 8.5 «kPa» ✔
Award [2] for bald correct answer.
Watch for POT mistakes.
the fluid speed at Y will be greater «than that at X» ✔
reducing the pressure at Y
OR
the formula used to show that the difference is increased ✔
Examiners report
Gasoline in a pipe. In a), most of the candidates well noted that for the Bernoulli equation, the fluid must be” non-viscous”, some noted, “laminar” and a few, “incompressible”. Some students stated vaguer and less concrete responses such as “the fluid must be ideal”.
In b) most candidates well noted and understood the application of the continuity equation.
In b) most candidates well noted and understood the application of the continuity equation and successfully went on to correctly calculate the pressure difference.
Sub-question iii) well discriminated between the better and weaker candidates. As weaker candidates often wrote that “lower diameter means higher pressure” without a direct reference to the greater speed at Y implying reduced pressure.
Syllabus sections
- 17N.3.SL.TZ0.11a.i: Identify the mechanism leading stars to produce the light they emit.
- 17N.3.SL.TZ0.11b.ii: Outline how the stellar parallax angle is measured.
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18M.3.HL.TZ1.10c.ii:
Outline whether it is reasonable to assume that flow is laminar in this situation.
- 19M.3.HL.TZ1.10b.i: Outline why the speed of the gasoline at X is the same as that at Y.
- 17N.3.SL.TZ0.11b.i: Outline what is meant by a constellation.
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17N.3.HL.TZ0.11a.i:
Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.
-
18M.3.HL.TZ1.10a:
State the difference in terms of the velocity of the water between laminar and turbulent flow.
-
18M.3.HL.TZ2.10b.i:
Estimate the Reynolds number for the fluid in your answer to (a).
- 18N.3.HL.TZ0.10b.i: Outline why u = 4v.
- 18N.3.HL.TZ0.10a: An ice cube floats in water that is contained in a tube. The ice cube melts. Suggest what...
-
19M.3.HL.TZ2.13a:
Draw and label the forces acting on the sphere at the instant when it is released.
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17M.3.HL.TZ1.9a:
Explain the origin of the buoyancy force on the air bubble.
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17M.3.HL.TZ2.10a.ii:
On the diagram, draw an arrow to indicate the direction of this force.
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17M.3.HL.TZ2.10a.i:
Estimate the magnitude of the force on the ball, ignoring gravity.
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17N.3.SL.TZ0.11a.ii:
Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.
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17N.3.SL.TZ0.11b.iii:
Show that the distance to Vega from Earth is about 25 ly.
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17N.3.HL.TZ0.11b:
The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m–3 to 785.16 kg m–3. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.
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17M.3.HL.TZ2.10b:
State one assumption you made in your estimate in (a)(i).
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18N.3.HL.TZ0.10b.ii:
The density of water is 1000 kg m–3. Calculate u.
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16N.3.HL.TZ0.13b:
Water flows through a constricted pipe. Vertical tubes A and B, open to the air, are located along the pipe.
Describe why tube B has a lower water level than tube A.
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17M.3.HL.TZ1.9b:
With reference to the ratio of weight to buoyancy force, show that the weight of the air bubble can be neglected in this situation.
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18M.3.HL.TZ1.10b:
The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.
Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = .
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19N.3.HL.TZ0.9a:
Explain why the levels of the liquid are at different heights.
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19M.3.HL.TZ1.10b.ii:
Calculate the difference in pressure between X and Y.
- 20N.3.HL.TZ0.12a: State two properties of an ideal fluid.
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20N.3.HL.TZ0.12c(iii):
Outline the effect on of changing the oil to one with greater viscosity.
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18M.3.HL.TZ1.10c.i:
Calculate the Reynolds number for the water flow.
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20N.3.HL.TZ0.12c(i):
Determine the force exerted by the spring on the sphere when the sphere is at rest.
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17M.3.HL.TZ1.9c:
Calculate the terminal speed.
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20N.3.HL.TZ0.12b:
Determine the terminal velocity of the sphere.
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16N.3.HL.TZ0.13a:
A solid cube of side 0.15 m has an average density of 210 kg m–3.
(i) Calculate the weight of the cube.
(ii) The cube is placed in gasoline of density 720 kg m–3. Calculate the proportion of the volume of the cube that is above the surface of the gasoline.
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17N.3.HL.TZ0.11a.ii:
When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m–3. Calculate the percentage of the sphere volume filled by water.
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19N.3.HL.TZ0.9b:
The density of the liquid in the tube is 8.7 × 102 kg m–3 and the density of air is 1.2 kg m–3. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.
- 19M.3.HL.TZ2.13b: Explain why the sphere will reach a terminal speed.
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19M.3.HL.TZ2.13c:
The weight of the sphere is 6.16 mN and the radius is 5.00 × 10-3 m. For a fluid of density 8.50 × 102 kg m-3, the terminal speed is found to be 0.280 m s-1. Calculate the viscosity of the fluid.
- 19M.3.HL.TZ1.10b.iii: The diameter at Y is made smaller than that at X. Explain why the pressure difference between...
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18M.3.HL.TZ2.10a:
Show that the velocity of the fluid at X is about 2 ms–1, assuming that the flow is laminar.
