Question

A 25 cm diameter pipe carries a oil of specific gravity 0.9 at a velocity of 3m/s. At another section diameter is 20 cm. Find the velocity at this section and mass rate of flow of oil.
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Answer 1

Answer:

the mean velocity of a laminar flow through a circular pipe of 30 cm is 15m/s. the local velocity of the flow at a radius of 25 cm is

Answer 2

Answer:

The velocity at the section is $4.687$ $m/s$. The mass rate of flow is $132.47$ $kg/s$.

Explanation:

• According to the equation of continuity, if the pipes are connected in series the discharge through one pipe is the same as the discharge through the other pipe.
• The mass rate of flow depends on the density of the liquid.

The formula used for the amount of liquid that flows in a second is:

$Q=A *v$

where $A$ is the cross-sectional area

           $v$ is the liquid's velocity.

Step 1:

Using the equation of continuity:

$A1*v1=A2*v2$

The cross-section area of the first pipe, $A1=\pi *(\frac{0.25^{2} }{4} )$ $m^{2}$

                                                                       $=0.015626\pi$ $m^{2}$

The cross-section area of the second pipe, $A2=\pi *(\frac{0.20^{2} }{4} )$ $m^{2}$

                                                                              $=0.01\pi$ $m^{2}$

Velocity at the first pipe, $v1= 3$ $m/s$

So, the velocity at the second pipe, $v2=\frac{(0.015625\pi *3)}{0.01\pi }$ $m/s$

                                                                $=4.687$ $m/s$

Step 2:

The mass rate of flow  $=density *A * v$

                                      $=(0.9*1000)kg/m^{3} *(0.015626\pi * 3)m^{3} /s$

                                      $=132.47$  $kg/s$

So, the velocity at the section is $4.687$ $m/s$.

The mass rate of flow is $132.47$  $kg/s$.