In the head loss formula h_L = (V1 - V2)^2 /(2g), which of the following expresses the correct units for h_L?

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Multiple Choice

In the head loss formula h_L = (V1 - V2)^2 /(2g), which of the following expresses the correct units for h_L?

Explanation:
Dimensional consistency shows why h_L is a length. V1 and V2 are velocities with units of meters per second (m/s); their difference is still m/s, and squaring gives m^2/s^2. The gravity term g has units of meters per second squared (m/s^2), and the factor 2 is dimensionless. So (V1 − V2)^2 /(2g) has units (m^2/s^2) / (m/s^2) = m. This means head loss represents a height, measured in meters in SI units. The other options correspond to time or velocity, not length.

Dimensional consistency shows why h_L is a length. V1 and V2 are velocities with units of meters per second (m/s); their difference is still m/s, and squaring gives m^2/s^2. The gravity term g has units of meters per second squared (m/s^2), and the factor 2 is dimensionless. So (V1 − V2)^2 /(2g) has units (m^2/s^2) / (m/s^2) = m. This means head loss represents a height, measured in meters in SI units. The other options correspond to time or velocity, not length.

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