Question

Water that has emerged from a hose into the atmosphere has a gauge pressure of zero. Why? When you put your hand in front of the emerging stream you feel a force, yet the water’s gauge pressure is zero. Explain where the force comes from in terms of energy.

Short answer

The water emerging from hose has atmospheric pressure. The kinetic energy of the air applies the force.

Step-by-step solution

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 h is the height.

Explanation for zero-gauge pressure.

Water emerging from hose has a gauge pressure of zero because the water coming out has a pressure of atmospheric pressure.

\({\rm{Gauge pressure}} = Absolute{\rm{ pressure}} - Atmospheric{\rm{ }}pressure\)

When the absolute pressure is equal to atmospheric pressure, the gauge pressure is zero.

Explanation for force from emerging stream.

The air that is present inside the hose has kinetic energy due to its motion. This kinetic energy is used to work against the pressure difference. So, the kinetic energy of the air applies the force which helps the water emerge from nozzle.