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Chapter 10: Q12Q (page 260)

Why does the stream of water from a faucet become narrower as it falls (Fig. 10鈥�43)?

FIGURE 10鈥�43 Question 12. Water coming from a faucet.

Short Answer

Expert verified

When the water is away from the faucet, the water velocity is greater and slower near the faucet. So, the cross-sectional area should be narrower when it falls.

Step by step solution

01

Understanding the application of continuity equation in the fluid flow

According to the continuity equation, the incompressible fluid having greater velocity has a lesser cross-sectional area and vice versa. The area of the cross-section and the velocity of the fluid are inversely related to each other.

02

Explaining the reason behind the stream of water from a faucet becomes narrower as it falls

As the water falls vertically, then the velocity of the water is greater near the surface of the Earth. And its velocity is lesser near the faucet.

The gravity effect is more significant near the surface of the Earth. The stream of water has a higher velocity near-surface of the Earth. Then, the cross-sectional area should be small or narrower.

That is why the stream of water from a faucet becomes narrower as it falls.

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Most popular questions from this chapter

A ship, carrying fresh water to a desert island in the Carib-bean, has a horizontal cross-sectional area of \(2240\;{{\rm{m}}^2}\) at the waterline. When unloaded, the ship rises 8.25 m higher in the sea. How much water \(\left( {{m^3}} \right)\) was delivered?

(II)Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 10-52).

In Fig. 10-54, take into account the speed of the top surface of the tank and show that the speed of fluid leaving an opening near the bottom is \({{\bf{v}}_{\bf{1}}}{\bf{ = }}\sqrt {\frac{{{\bf{2gh}}}}{{\left( {{\bf{1 - A}}_{\bf{1}}^{\bf{2}}{\bf{/A}}_{\bf{2}}^{\bf{2}}} \right)}}} \),

where \({\bf{h = }}{{\bf{y}}_{\bf{2}}} - {{\bf{y}}_{\bf{1}}}\), and \({{\bf{A}}_{\bf{1}}}\) and \({{\bf{A}}_{\bf{2}}}\) are the areas of the opening and of the top surface, respectively. Assume \({{\bf{A}}_{\bf{1}}}{\bf{ < < }}{{\bf{A}}_{\bf{2}}}\) so that the flow remains nearly steady and laminar.

Figure 10-54

(II)What is the lift (in newtons) due to Bernoulli鈥檚 principle on a wing of area\(88\;{{\rm{m}}^2}\)if the air passes over the top and bottom surfaces at speeds of 280 m/s and 150 m/s, respectively?

Hot air is less dense than cold air. Could a hot-air balloon be flown on the Moon, where there is no atmosphere?

(a) No, there is no cold air to displace, so no buoyancy force would exist.

(b) Yes, warm air always rises, especially in a weak gravitational field like that of the Moon.

(c) Yes, but the balloon would have to be filled with helium instead of hot air.
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