Question

A smooth pipe of diameter 500 mm carries water. The pressure in the pipe at Section ‘A’ (elevation: 10 m) is 100 kPa. At section ‘B’ (elevation: 12 m) the pressure is 75 kPa and velocity is 4 m/s. Which of the following is true (g = 10 m/s²)
1. Flow from A to B and head loss is 1 m
2. Flow from A to B and head loss is 0.5 m
3. Flow from B to A and head loss is 0.5 m
4. Flow from B to A and head loss is 0.75 m

Answer 1

Correct Answer - Option 2 : Flow from A to B and head loss is 0.5 m

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:

P₁ = 100 kPa, Z₁ = 10 m, P₂ = 75 kPa, z₂ = 12 m, v = 4 m/s, d = 500 mm = 0.5 m

At Section 1 

\(\frac{{{p_1}}}{{\rho g}} + \frac{{V_1^2}}{{2g}} + {z_1} = \frac{{100 \times {{10}^3}}}{{1000 \times 10}} + \frac{{{4^2}}}{{2 \times 10}} + 10 = 20.8\;m\)

At Section 2

\(\frac{{{p_2}}}{{\rho g}} + \frac{{V_2^2}}{{2g}} + {z_2} = \frac{{75 \times {{10}^3}}}{{1000 \times 10}} + \frac{{{4^2}}}{{2 \times 10}} + 12 = 20.3\;m\)

(Total Energy) 1 > (Total Energy) 2

∴ Flow takes place from section 1 to section 2 with a head loss of 0.5 m.