Fluids and Density: Worked Solutions

Try the questions on the lesson page first. Then compare both the answer and the reasoning. The worked steps here are original.

Question 1: Two samples of the same uniform liquid have volumes V and 3V at the same conditions. Their densities…

Two samples of the same uniform liquid have volumes V and 3V at the same conditions. Their densities…

1. Use density ρ = m/V. Why: Density compares mass with the volume containing it.
2. For the same uniform liquid at fixed conditions, tripling V triples m. Why: The composition and density remain the same in the stated comparison.
3. Their ratios m/V are equal. Why: Increasing sample size changes total mass, not the material density.

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Question 2: A graph has liquid mass on the vertical axis and volume on the horizontal axis. Its slope is…

A graph has liquid mass on the vertical axis and volume on the horizontal axis. Its slope is…

1. Read the graph axes: mass vertically and volume horizontally. Why: Slope means change in the vertical quantity divided by change in the horizontal quantity.
2. Form slope = Δm/ΔV. Why: This has mass-per-volume units.
3. Identify the slope as density ρ. Why: The relationship m = ρV predicts this slope for a uniform liquid.

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Question 3: Which pair defines the ideal-fluid model here?

Which pair defines the ideal-fluid model here?

1. Incompressible means a fixed amount keeps its volume and density. Why: This allows the same density to be used throughout the ideal-flow calculation.
2. Nonviscous means internal frictional dissipation is neglected. Why: This is the second assumption needed for the ideal fluid model here.
3. Choose incompressible and nonviscous. Why: Fixed shape is a solid-like feature and is not part of the ideal-fluid definition.

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Question 4: the container intercept

A best-fit total-mass graph obeys m_total = (0.90 g/mL)V + 45 g. Find the liquid density in SI units and explain what the intercept means. What total mass should the balance show for 60 mL?

1. Read the slope 0.90 g/mL as liquid density, then convert to 900 kg/m³. Why: One g/mL is 1000 kg/m³; slope measures added liquid mass per added volume.
2. Identify the 45 g intercept as empty container mass. Why: At V = 0 the fitted total mass is the container alone.
3. At 60 mL compute m_total = 0.90(60) + 45 = 99 g. Why: The balance records both liquid and container. Dividing 99 g by liquid volume would incorrectly include the container in density.

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