A water tank is filled to a depth of 10 m,and the bottom of the tank is 20 m above ground.A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground,but no water is flowing in this hose.The water pressure at ground level in the hose is closest to which of the following values? The density of water is 1000 kg/m³. A)3.9 × 10⁵ N/m² B)2.0 × 10⁴ N/m² C)9.2 N/m² D)The question cannot be answered because the cross sectional area of the tank is needed.

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Quizplus · Accepted Answer

The pressure at the bottom of the tank is due to the weight of the water above it. The pressure at ground level is the pressure at the bottom of the tank plus the pressure due to the weight of the water in the hose. The pressure due to the weight of the water in the hose is:$$P = ho g h$$where:* $ ho$ is the density of water (1000 kg/m³)* $g$ is the acceleration due to gravity (9.8 m/s²)* $h$ is the height of the water in the hose (20 m)Plugging in these values, we get:$$P = (1000 ext{ kg/m}^3)(9.8 ext{ m/s}^2)(20 ext{ m}) = 1.96 imes 10^5 ext{ N/m}^2$$Adding this to the pressure at the bottom of the tank, we get:$$P = 1.96 imes 10^5 ext{ N/m}^2 + 3.9 imes 10^5 ext{ N/m}^2 = 3.9 imes 10^5 ext{ N/m}^2$$Therefore, the water pressure at ground level in the hose is closest to 3.9 × 10⁵ N/m².

A Water Tank Is Filled to a Depth of 10