This is a really simple demonstration that allows you to measure the specific gravity of oil using a u-tube manometer. It also gives students the opportunity to visualize a multi-fluid manometer.

**Equipment**

- A 4 foot length of clear flexible tubing with a diameter of about a half to one inch
- A funnel
- A bucket of water
- A jug of oil (cheap cooking oil is perfect)
- A tape measure or ruler
- A chalk or white board with appropriate marker.
- A student volunteer

**Demonstration**

- Draw a horizontal line on the board.
- Hold the tubing at each end forming a u-tube.
- Have the student pour water into the tube until there is about 9 inches of air between the top of the water and the top of the tube ends
- Show the students that the water levels are at the same height on both sides of the u-tube
- Have the student slowly pour the oil into one side of the u-tube until there is about 2-3 inches of air between the top of the oil and the top of the tube.
- Hold the u-tube up so that the bottom of the column of oil is at the height of the line drawn on the board.
- Measure the height of the column of oil (H
_{oil}) and the height of the water (H_{water}) above the same horizontal line.

**Analysis**

Because hydrostatic pressure does not vary horizontally across the connected water, the pressure in the u-tube at the height of the line on the board is the same on both sides. Starting at the oil free surface you can write that the pressure at the line is

P_{line}=ρ_{oil }g H_{oil}

The pressure at the line can also be calculated starting at the free surface of the water,

P_{line}=ρ_{water }g H_{water}

Equating these two pressures gives

P_{line}=ρ_{water }g H_{water}=ρ_{oil }g H_{oil}

which can be re-written as

S.G._{oil}=ρ_{oil}/ρ_{water}= H_{water}/H_{oil}

For the example in the pictures the depths were H_{water}=15cm and H_{oil}=18cm such that S.G._{oil}=0.83. You can then compare this to online data tables for various oil densities.

The demonstration is also good for discussing measurement errors as there is error in both height measurements. Re-doing the S.G. calculation with, for example, the low estimate of H_{oil} and the high estimate of H_{water} (or vice versa) will give a different result. In this case the uncertainty in the measurement is at least 0.5 cm so the S.G ranges from 0.78 to 0.89.

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can you help me with the experiment of determine the relative density of oil