Answer to Question #111215 in Mechanical Engineering for george H

Question

(A) A 250 mm diameter pipe carries water flowing at 87 litres per second. the main pipe divides into two pipes,each 100 mm diameter. calculate the velocity in the smaller pipes.

(B) Evaluate the nature of linear momentum principles and their application in determining fluid flow parameters in optimising the operation of nozzle systems and fluid turbines.

Answer 1

(A) Diameter of large pipe cross section=250 mm

and the flow rate through that pipe= 87 l/sec= $87 \times 10^{-3} \frac{m^3}{s}$

Q=av, Q= flow rate

$Q= a_1v_1=87 \times 10^{-3} \frac{m^3}{s}$

$v_1=\frac{87 \times 10^{-3} \frac{m^3}{s}}{a_1}$

As per equation of continuity flow rate remain same

so, as per the question pipe divide in two equal diameter so velocity in both pipe remain same and thus we can say that,

$a_1v_1= 2\times a_2\times v_2$

$a_1\times \frac{87 \times 10^{-3} \frac{m^3}{s}}{a_1}= 2\times (\frac{\pi}{4})\times (0.01)^2 \times v_2$

$v_2=$ 5.54 m/s

(B) As per the conservation of momentum momentum remain conserved and due this principle the fluid exert pressure force in two direction i.e in vertical direction and in horizontal direction

and nozzle is a device which converts the energy from a fluid into velocity of the spray droplets.