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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Water is shot nearly vertically upward in a decorative fountain and the stream is observed to broaden as it rises. Conversely, a stream of water falling straight down from a faucet narrows. Explain why, and discuss whether surface tension enhances or reduces the effect in each case.

The fluid velocity increases when the area of the cross-section is decreased and vice versa.

See the step by step solution

## Step 1: Tension

A force over the length of a medium, particularly a force carried by a flexible medium like a rope or cable, is known as tension.

## Step2: Water shot nearly vertically upward

When water is shot vertically upwards, the gravity of the earth acts on it. The gravity decreases the fluid velocity more and more as it travels vertically upward. Water is incompressible and the flow rate remains constant. As the flow rate is constant and velocity is decreasing, the area must increase as per the continuity equation. The increase in area broadens the stream of the water.

## Step 3: Effect of smaller cross-sectional area

When a stream of water is falling straight down from the faucet, the gravity of the earth acts on it. The gravity increases the fluid velocity more and more as it travels downward. Water is incompressible and the flow rate remains constant. As the flow rate is constant and velocity is increasing, the area must decrease as per the continuity equation. The decrease in area narrows the stream of water.

## Step4: Effect of surface tension

The water tries to minimize its surface area. The surface tension reduces the effect of stream broadening when it is shot vertically. The surface tension increases the stream narrowing when water is falling down.