Pressure: 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: Pressure is a scalar. Which statement follows?

Pressure is a scalar. Which statement follows?

1. Pressure is force magnitude per area and has no direction. Why: The ratio F_perpendicular/A uses the normal force magnitude and surface area; it gives a pressure value without assigning a direction.
2. For a resting fluid, the pressure force acts normal to each surface. Why: The surface orientation supplies the direction of that force.
3. Choose the statement that separates scalar pressure from directed force. Why: A scalar can set the magnitude of a vector force without becoming a vector itself.

Try this question again.

Question 2: An open pool has zero gauge pressure at its surface. Its absolute pressure there is…

An open pool has zero gauge pressure at its surface. Its absolute pressure there is…

1. Use P_absolute = P_atmosphere + P_gauge. Why: Gauge pressure is measured relative to the atmosphere in this open-pool case.
2. At the surface, insert P_gauge = 0. Why: No fluid depth has been added below the chosen reference level.
3. Absolute pressure equals atmospheric pressure. Why: Subtracting the reference to make a gauge reading does not remove the actual atmosphere.

Try this question again.

Question 3: A gauge-pressure-versus-depth graph for a uniform resting fluid has slope…

A gauge-pressure-versus-depth graph for a uniform resting fluid has slope…

1. Start with P_gauge = ρgh. Why: Hydrostatic balance gives the pressure difference below the surface.
2. Hold ρ and g constant. Why: The question specifies one uniform resting fluid.
3. The slope versus h is ρg, in Pa/m. Why: Container bottom area cancels in the force-balance derivation.

Try this question again.

Question 4: a submerged window

A small horizontal window of area 0.020 m² is 1.5 m below an open water surface. Air behind it is at the same atmospheric pressure as the surface. Approximate the pressure as uniform over the window. Find the net pressure force and explain why using absolute water pressure alone would be wrong.

1. Subtract inside atmospheric pressure from outside pressure to get ΔP = ρgh = (1000)(9.8)(1.5) = 14,700 Pa. Why: The same atmospheric reference appears on both sides and cancels.
2. Use net force magnitude ΔPA = (14,700)(0.020) = 294 N. Why: The pressure difference acts over the stated area; forces on opposite sides point oppositely.
3. The force points from water toward the air side, normal to the window. Why: Pressure is scalar, but the window orientation and which side has greater pressure determine the force direction. Absolute water pressure alone would omit the air force.

Try this written problem again.