Question

When water flows through a pipe that gets narrower, what happens to the speed of the water?.

Answer 1

Therefore, the speed of the liquid increases as it passes through the constriction. Since the meter is assumed to be horizontal.

Thus, as the fluid passes through the constriction or throat, the higher speed results in lower pressure at the throat. The expression for the continuity equation is,

A1v1=A2v2

Here, A1andA2 are the cross-sectional areas at the inlet and outlet, respectively, and

V1, V2  are the velocity of the fluid at the inlet and outlet, respectively

Let,

A1

and A2be the cross-sectional areas at point 1 and 2, respectively, andv1, v2be the corresponding flow speed.

Express the relation for the continuity equation.

A1v1=A2v2..........................(1)

Now apply proportionate rule,

v2v1=A1A2>1(∵A1>A2)

Therefore, the speed of the liquid increases as it passes through the constriction. Since the meter is assumed to be horizontal.

Now, according to Bernoulli’s equation, we get,

p1+12ρv12=p2+12ρv22p1−p2=12ρ[v22−v12]p1−p2=12ρv12[(v2v1)2−1]p1−p2=12ρv12[(A1A2)2−1]​

Again, Since

A1>A2

the bracketed term is positive, so thatp1>p2. Thus, as the fluid passes through the constriction or throat, the higher speed results in lower pressure at the throat.

Answer 2

Answer:

The impact of the continuity equation may be seen in a garden hose. Water travels through the hose, increasing in velocity as it approaches the narrower nozzle. When the cross-sectional area reduces, the speed rises, and when the cross-sectional area grows, the speed drops.

Explanation: