A small swimming pool is drained using a garden hose. The hose has 20 mm inside diameter, a roug

step 1 By using Bernoulli equation we can write the head loss equation as P1 divided by Rho plus B1 squ

A small swimming pool is drained using a garden hose. The...

A small swimming pool is drained using a garden hose. The hose has $20 \mathrm{mm}$ inside diameter, a roughness height of $0.2 \mathrm{mm},$ and is $30 \mathrm{m}$ long. The free end of the hose is located $3 \mathrm{m}$ below the elevation of the bottom of the pool. The average velocity at the hose discharge is $1.2 \mathrm{m} / \mathrm{s}$. Fstimate the depth of the water in the swimming pool. If the flow were inviscid, what would be the velocity?

Key Concepts

Bernoulli's Principle

Bernoulli's principle is a statement of energy conservation for flowing fluids. It relates pressure energy, kinetic energy, and potential energy per unit volume along a streamline, and is used to determine how changes in elevation or fluid velocity lead to corresponding changes in fluid pressure.

Darcy-Weisbach Equation

The Darcy-Weisbach equation quantifies the head loss due to friction in pipe flow. It links the frictional losses to factors such as the length and diameter of the pipe, the fluid’s velocity, and the friction factor, thereby allowing calculation of energy dissipation in a real (viscous) fluid flowing through conduits.

Friction Factor and Pipe Roughness

The friction factor is a dimensionless parameter that incorporates the effects of pipe roughness and the Reynolds number of a flow to determine the resistance to flow in a pipe. It is crucial in calculating head losses and understanding whether the flow is in a laminar or turbulent regime.

Torricelli's Law

Torricelli's law provides an expression for the velocity of fluid flowing under the influence of gravity from an orifice in an ideal (inviscid) fluid system. Derived from the conservation of energy, it relates the fluid exit speed to the square root of twice the gravitational acceleration times the height of the fluid above the exit point.

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