Question

The density of water is assumed to be a constant of 1000 kg/m^3. If the gage pressure of a water column 10 m high is 10 kPa, then the gage pressure of a water column 30 m high should be 20 kPa 30 kPa 40 kPa 50 kPa 10 kPa

Answer 1

The gage pressure for a 30 m high water column, assuming a density of 1000 kg/m³ and gravity of 9.81 m/s², would be 30 kPa, since pressure is directly proportional to height.

Step-by-step explanation:

The question involves the calculation of the gauge pressure of a water column at different heights using the principles of fluid mechanics in physics. The formula for hydrostatic pressure, P = hρg, where P is the pressure, h is the height of the water column, ρ (rho) is the density of the fluid, and g is the acceleration due to gravity, is used to determine the pressure exerted by the water column.

For a 10 m high water column with a density of 1000 kg/m³ and an acceleration due to gravity of approximately 9.81 m/s², the gage pressure is given as 10 kPa. Considering the formula, if the height of the water column increases to 30 m (three times the original height), the gage pressure will also triple, because height is directly proportional to pressure when the other variables remain constant. Using the direct proportionality, the gage pressure for a 30 m high water column would be 30 kPa. Thus, the correct option in the final answer is 30 kPa.