Question

Consider the following statements:

A horizontal pipe reduces from 10 cm to 5 cm in diameter. If the pressure head at 10 cm section is 10 metres and velocity head is 1 metre, then the

1. Total head at any point is 11 metres

2. Pressure head at the 5 cm section is negative

3. Discharge varies proportionate to the diameter

4. Datum head at all sections is constant

Which of these statements is/are correct?

• A. 1, 2 and 4
• B. 1 and 3
• C. 4 alone
• D. 1, 2, 3 and 4

Answer 1

The correct option is A 1, 2 and 4

Total head is given by

$H_1=Z_1+\frac{p_1}{\rho g}+\frac{V_1^2}{2g}$

$=10+1=11\text{m}$

at 10 cm section. For horizontal pipe datum head will remain same.

$\text{Discharge}Q=VA=V\left(\frac{\pi D^2}{4}\right)$

Discharge is proportional to square of diameter. From continuity equation discharge does not vary from 10 cm section to 5 cm section.

$V_1{A}_1=V_2{A}_2$

$\therefore \text{Velocity at 5 cm section,}$

$V_2=V_1\times {\left(\frac{10}{5}\right)}^2=4V_1$.

Velocity head at 5 cm section

$=\frac{V_2^2}{2g}=\frac{16V_1^2}{2g}=16m$

Using Bernoulli's equation, we get

$\frac{p_1}{\rho g}+\frac{V_1^2}{2g}=\frac{p_2}{\rho g}+\frac{V_2^2}{2g}$

$\frac{p^2}{\rho g}=11-16=-5m$

Thus pressure head at 5 cm section is negative.