Equation Of Continuity

Question

Water flowing through a horizontal pipe has a speed of 3 m/s in a section of cross-sectional area $6\,	ext{cm}^2$. When the pipe widens to a cross-sectional area of $18\,	ext{cm}^2$, what is the speed of the water in the wider section?

RankGuru · Accepted Answer

For an incompressible fluid in steady flow, mass is conserved so the same volume passes every cross-section each second, expressed by the equation of continuity $A_1v_1 = A_2v_2$. This means the product of area and speed is constant, so a wider pipe forces the fluid to slow down while a narrower pipe speeds it up. Solving for the speed in the wide section, $v_2 = v_1\frac{A_1}{A_2} = 3	imes\frac{6}{18} = 3	imes\frac{1}{3} = 1\,	ext{m/s}$. The value 3 m/s ignores the change in area. The value 6 m/s wrongly increases the speed where the pipe widens. The value 9 m/s multiplies instead of using the inverse area ratio. This conservation-of-mass relation is exactly the equation of continuity presented in NCERT for fluid dynamics. As a plausibility check, since the cross-section triples, the speed must fall to one-third to keep the volume flow rate constant, and the obtained 1 m/s indeed gives the same flow rate of $1800\,	ext{cm}^3/	ext{s}$ as the original section.

Equation Of Continuity

Select the correct option:

🔒 Solution Hidden from View

More properties of solids and liquids Practice Questions

If the absolute temperature of a perfectly black body radiating heat is doubled, by what factor does...

In a hydraulic lift the small piston has an area of 0.01 m² and the large piston has an area of 0.5 ...

A metal rod of length 1 m at 20°C has a coefficient of linear expansion of 2 \times 10^{-5} per °C; ...

How much heat energy must be supplied to raise the temperature of 0.5 kg of water from 25°C to 75°C,...

When a substance is melting at its melting point while heat is continuously supplied, what happens t...

Two metal rods of identical length and cross-section but different thermal conductivities are joined...

A hot body cools from 80°C to 70°C in 5 minutes when placed in surroundings at 30°C; according to Ne...

A diver descends to a depth of 20 m below the surface of a lake where water density is 1000 kg/m³; w...

A wire is stretched so that it stores elastic potential energy; if the same wire is stretched to twi...

The Reynolds number is used to predict the nature of fluid flow in a pipe; a very high Reynolds numb...

During winter a lake freezes only at its surface while fish survive in the water below; this is best...

A steel wire of length 2 m and cross-sectional area 1 mm² is stretched by a load of 100 N, producing...

About This Question

Solution