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College Physics (Urone)
Found in: Page 426

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Short Answer

Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.

Water emerges from the nozzle due to the difference in pressure energy and kinetic energy.

See the step by step solution

Step by Step Solution

Step 1: Concept of Bernoulli’s equation.

Bernoulli’s equation is the relationship between pressure and velocity in fluids. It states that for an incompressible fluid, the following sum is constant.

\(P + \frac{1}{2}\rho {v^2} + \rho gh = {\rm{constant}}\)

Here, P is the pressure, v is the velocity, \(\rho \) is the density, g is the acceleration due to gravity, and is the height.

Step 2: Explanation for water emerging from nozzle.

According to Bernoulli’s principle, the sum of pressure energy, kinetic energy, and potential energy between two points is constant. So, when the pressure inside the hose nozzle is less than the atmospheric pressure then the velocity of water in a hose nozzle is greater than the velocity of water at atmosphere.

Here, hose nozzle is one point and the atmosphere be the other point. Consider the potential energy to be same between two points, then when the pressure energy is less at point 1 than at point 2 then the kinetic energy at point 1 would be greater than at point 2. This enables water emerge from the nozzle against the atmospheric pressure.

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