At point A in a pipeline carrying water, the diameter is 1 m, the
A. A to B
B. B to A
C. Cannnot be ascertained from data
D. None of these
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
To find the direction of flow of water, we have to calculate energy at each end.
So, the energy at each is given as, \(E = \frac{P}{{\rho g}} + \frac{{{V^2}}}{{2g}}+ z\)
Calculation:
Given:
At point A
DA = 1 m, PA = 98 kPa, VA = 1 m/s, zA = 0
At point B
DB = 0.5 m, PB = 20 kPa, zB = 2 m
Energy at point A:
\(E_A = \frac{{98 \times {{10}^3}}}{{10 \times 1000}} + 0 + \frac{{{1^2}}}{{2 \times 10}}\)
EA = 9.85 m
Now for velocity at B, applying continuity equation
AAVA = ABVB
\(\frac{\pi }{4}D_1^2{V_1} = \frac{\pi }{4}D_2^2.{V_2} \Rightarrow 1 \times 1 = {\left( {0.5} \right)^2} \times {{\rm{V}}_2}\)
⇒ VB = 4 m/s
Energy at point B:
\({E_B} = \frac{{20 \times {{10}^3}}}{{10 \times 1000}} + 2 + \frac{{{4^2}}}{{20}}\)
EB = 4.8 m
From the energy at both points, EA > EB. So flow will take place from A to B
