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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

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

Question: A simple model (Fig. 10鈥�56) considers a continent as a block (density\( \approx {\bf{2800}}\;{\bf{kg/}}{{\bf{m}}^{\bf{3}}}\)) floating in the mantle rock around it (density\( \approx {\bf{3300}}\;{\bf{kg/}}{{\bf{m}}^{\bf{3}}}\)). Assuming the continent is 35 km thick (the average thickness of the Earth鈥檚 continental crust), estimate the height of the continent above the surrounding mantle rock.

Figure 10-56

A drinking fountain shoots water about 12 cm up in the air from a nozzle of diameter 0.60 cm (Fig. 10鈥�57). The pump at the base of the unit (1.1 m below the nozzle) pushes water into a 1.2-cm-diameter supply pipe that goes up to the nozzle. What gauge pressure does the pump have to provide? Ignore the viscosity; your answer will therefore be an underestimate.

Question: A hydraulic lift is used to jack a 960-kg car 42 cm off the floor. The diameter of the output piston is 18 cm, and the input force is 380 N. (a) What is the area of the input piston? (b) What is the work done in lifting the car 42 cm? (c) If the input piston moves 13 cm in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up 42 cm? (e) Show that energy is conserved.

Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 4.0000 kg when weighed in air.
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