Water flows up a tapered pipe and at two sections 1 and 2, the fo
Water flows up a tapered pipe and at two sections 1 and 2, the following details were given.
At section 1: Pressure = 200 kPa, Elevation = 0 m, Diameter = 10 cm, Velocity = 4 m/s,
At section 2: Elevation = 10 m, Diameter = 20 cm;
The pressure at section 2 is
A. 107.5 kPa
B. 307.5 kPa
C. 207.5 kPa
D. 157.5 kPa
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
Bernoulli’s Equations
At Section 1
\(\frac{{{p_1}}}{{\rho g}} + \frac{{V_1^2}}{{2g}} + {z_1}\)
At Section 2
\(\frac{{{p_2}}}{{\rho g}} + \frac{{V_2^2}}{{2g}} + {z_2}\)
Calculation:
Given Data:
P1 = 30 kPa, Z1 = 0, V1 = 4 m/s; Z2 = 10 m, D2 = 20 cm;
From continuity, A1 V1 = A2 V2
⇒ 10 × 10 × 4 = 20 × 20 × V2
⇒ V2 = 1 m/s;
At Section 1
\(\frac{{{p_1}}}{{\rho g}} + \frac{{V_1^2}}{{2g}} + {z_1} = \frac{{200 × {{10}^3}}}{{1000 × 10}} + \frac{{{4^2}}}{{2 × 10}} + 0 = 20.8 \;m\)
At Section 2
\(\frac{{{p_2}}}{{\rho g}} + \frac{{V_2^2}}{{2g}} + {z_2} = \frac{{P × {{10}^3}}}{{1000 × 10}} + \frac{{{1^2}}}{{2 × 10}} + 10 = 20.8\;m\)
⇒ P = 107.5 kPa