Single Choice

An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom $${p}_{2}$$ is the same as it is at the top $${p}_{1}$$. If the velocity of the top $${ v }_{ 1 }=m/s$$. Then the ratio of areas $${A}_{1}$$. $${A}_{2}$$ is

A$$2:1$$
B$$4:1$$
Correct Answer
C$$8:1$$
D$$4:3$$

Solution

$${ P }_{ 1 }+\dfrac { 1 }{ 2 } { \rho V }_{ 1 }^{ 2 }+0={ P }_{ 2 }+\dfrac { 1 }{ 2 } { \rho V }_{ 2 }^{ 2 }-\rho g\left( 3 \right) $$
$$\Rightarrow \frac { 4 }{ 2 } +30=\dfrac { 1 }{ 2 } { V }_{ 2 }^{ 2 }$$
$$\Rightarrow { V }_{ 2 }=8m/s$$
Now according to torrlcellis theorem
$${ A }_{ 1 }{ V }_{ 1 }={ A }_{ 2 }{ V }_{ 2 }$$
$$\dfrac { { A }_{ 1 } }{ { A }_{ 2 } } =\dfrac { 8 }{ 2 } =4:1$$

SIMILAR QUESTIONS

Fluid Mechanics

Pressure head in Bernoulli's equation is:

Fluid Mechanics

Bernoulli's equation is conservation of:

Fluid Mechanics

Bernoulli's principle is based on the law of conservation of :

Fluid Mechanics

A body weighs $$5\ N$$ in air and $$2\ N$$ when immersed in a liquid. The buoyant force is

Fluid Mechanics

Demonstrate that in the case of a steady flow of an ideal fluid $$Eq.(1.7a)$$ turn into Bernoulli equation.

Fluid Mechanics

In the case of a fluid, Bernoulli's theorem expresses the application of the principle of conservation of:

Fluid Mechanics

The pressure difference across a pipe of length $$5 cm$$ is $$2\times10^{3}Pa$$. Work done by the pressure in forcing $$2m^{3}$$ of water through the pipe in joule is :

Fluid Mechanics

The Bernoulli's equation that is valid for non-viscous, incompressible fluids having laminar flow is a consequence of

Fluid Mechanics

The velocity of a kerosene oil in a horizontal pipe is $$5 m/s$$. If $$g = 10 m/s^2$$ then the velocity head of oil will be

Fluid Mechanics

State and prove Bernoulli's theorem.

Contact Details