Question

Water flowing through a pipe of 5cm diameter under a pressure of 29.43 n/cm2 (gauge) and with mean velocity of 2.0 m/s. Find the piezometric head of the water at a cross-section which is 5 m above the datum line. (in m)

Answer 1

Given:

According to the question, water flowing through a pipe.

The dimensions of the pipe are:

Diameter of the pipe $= 5 cm$

Pressure $=29.43\text{ }n/cm^2\text{ }\left( gauge \right)$ $=29.43\times {{10}^{4}}N/{{m}^{2}}$

Velocity $=2m/s$                                

Datum head $=5m$                      

To find:

We need to find the piezometric head of the water.

Solution:

Piezometric head is nothing but, it is the addition of the pressure head at any point and datum head or also called as elevation head.

So, the value of Piezometric head = Pressure head + Datum head.

So, Total head = pressure head + kinetic head + datum head

Also,

Pressure head $=P/\rho g$

                         $=29.43\text{}\times104\text{}/1000\text{ }\times9.81\text{ }=30m$

Kinetic head $={{v}^{2}}/2g$

                     $={{2}^{2}}/2\times 9.81 \frac{4}{2\times 9.81}=0.204m$      

Datum head $=5m$

Therefore, Total head $=P/\rho g+{{v}^{2}}/2g+z$

                                     $=30+0.204+5$

                                     $= 35.204m$

Answer 2

what is 104 and 0.204 how you get