Water is pumped through a pipe of diameter 15.0 cm, from the Colorado River up to Grand Canyon Village, located on the rim of the canyon. The river is at an elevation of 564 m, and the village is at an elevation of 2096 m. What is the minimum pressure at which the water must be pumped if it is to arrive at the village?

Question

Physics

Bugsy

20 August, 08:59

Water is pumped through a pipe of diameter 15.0 cm, from the Colorado River up to Grand Canyon Village, located on the rim of the canyon. The river is at an elevation of 564 m, and the village is at an elevation of 2096 m. What is the minimum pressure at which the water must be pumped if it is to arrive at the village?

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Answers (1)

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Denzel · Answer 1

p = 1.50289*10⁷ N/m²

Explanation:

Given

HA = (564 m) ... (River Elevation)

HB = (2096 m) ... (Village Elevation)

Area = A = (π/4) {Diameter}² = (π/4) {0.15 m}² = 0.017671 m²

ρ = (1 gram/cm³) = (1000 kg/m³) ... (Water Density)

p (pressure) = ?

Solution

p=PA - PB

p = ρ*g*HB - ρ*g*HA

p = (ρ*g) * (HB - HA)

p = (1000*9.81) * {2096 - 564}

p = 1.50289*10⁷ N/m²