Question

Water flows through a horizontal pipe. The area of cross section at one place A1 = 10cm^2. The velocity of water is 1m/s and pressure is 2000pa at the same place. Find the velocity and pressure at another place of area A2 = 5cm^2

Answer 1

The velocity and pressure at another place are 2 m/s and 500 Pa respectively.

Explanation:

To calculate the velocity of water at the other end of pipe, use equation of continuity as

$A_{1} v^2_{1} =A_{2} v^2_{2}$

Here, $A_{1}$ is the area of the cross section at one end of the pipe and $A_{2}$ is the area of the cross section at the other end of the pipe $v_{1}$ and $v_{2}$ are the velocities separate ends.

Given $A_{1}=10cm^2$,  $A_{2}=5cm^2$ and $v_{1} =1m/s$.

Substitute the given values, we get

$10\times 10^{-2} m^2\times1m/s=v_{2}\times5\times10^{-2} m^2$

$v_{2}=2m/s$

Now to calculate the pressure at another end, use Bernoulli's theorem as

$P_{1}+\frac{1}{2}dv^2_{1} = P_{2}+\frac{1}{2}dv^2_{2}$

Here, d is the density of the water and it value is $1000 kg/m^3$ and given $P_{1} =2000Pa$.

Substitute the given values, we get

$2000Pa+\frac{1}{2} \times1000kg/m^3\times 1^{2}m/s=P_{2} +\frac{1}{2} \times1000kg/m^3\times 2^{2}m/s$

$P_{2}=500 Pa$

Thus, the velocity and pressure at another place are 2 m/s and 500 Pa respectively.

#Learn More:

Topic :equation of continuity and Bernoulli's theorem.

https://brainly.in/question/1827471

Answer 2

Explanation:

a1v1=a2v2

a1=10cm^2

a2=5cm^2