---
title: "Branch pipe diameters from a single feeder (f 0.024)"
subject: "Hydraulics"
chapter: 3
key: "semester_4/hydraulics:reservoir-feeds-two-reservoirs-branch-f024"
source: https://www.bctengineer.com/q/semester_4/hydraulics/reservoir-feeds-two-reservoirs-branch-f024
site: BCT Engineering
---

# Branch pipe diameters from a single feeder (f 0.024)

Hydraulics · Chapter 3: Three reservoirs problem and Pipe networks

- Asked in: 2076 Baisakh, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/reservoir-feeds-two-reservoirs-branch-f024
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-3

## Question

A reservoir A feeds two lower reservoirs B and C through a single pipe 10 km long, 750 mm diameter, having a downward slope of $2.2\times10^{-3}$. This pipe then divides into two branch pipes, one 5.5 km long laid with a downward slope of $2.75\times10^{-3}$ (going to B), the other 3 km long having a downward slope of $3.2\times10^{-3}$ (going to C). Calculate the necessary diameter of the branch pipes so that the steady flow rate in each shall be 0.24 m³/s when the level in each reservoir is 3 m above the end of the corresponding pipe. Neglect all losses except pipe friction and take f = 0.024 throughout.

## Short answer

Main pipe friction loss = 19.25 m, H_J = 5.75 m. Available heads: to B 17.87 m, to C 12.35 m. Using D = (8fLQ²/(π²g h_f))^(1/5) gives D_B ≈ 512 mm, D_C ≈ 488 mm.

## Answer

**Data.** Main pipe AJ: $L = 10$ km, $D = 0.75$ m, slope $2.2\times10^{-3}$. Branch JB: $L = 5.5$ km, slope $2.75\times10^{-3}$. Branch JC: $L = 3$ km, slope $3.2\times10^{-3}$. $Q_B = Q_C = 0.24$ m³/s, so the main pipe carries $Q = 0.48$ m³/s. $f = 0.024$. Only friction loss: $h_f = \dfrac{8fLQ^2}{\pi^2gD^5}$. Each reservoir level is 3 m above the end of its pipe (A: above the start of the main pipe; B and C: above the ends of the branches).

#### Elevations (datum: level of junction J)
- The main pipe falls $10\,000(2.2\times10^{-3}) = 22$ m from A to J, so the level of A is $22 + 3 = 25$ m above J.
- The branch to B falls $5500(2.75\times10^{-3}) = 15.125$ m, so the level of B is $-15.125 + 3 = -12.125$ m (12.125 m below J).
- The branch to C falls $3000(3.2\times10^{-3}) = 9.6$ m, so the level of C is $-9.6 + 3 = -6.6$ m.

#### Head loss in the main pipe and the head at J
$$
h_{f,AJ} = \frac{8(0.024)(10\,000)(0.48)^2}{\pi^2(9.81)(0.75)^5} = 19.25\ \text{m}
$$
Piezometric head at J (above J's level): $H_J = 25 - 19.25 = 5.75$ m.

#### Head available for each branch
- To B: $h_B = H_J - (-12.125) = 17.87$ m
- To C: $h_C = H_J - (-6.6) = 12.35$ m

#### Branch diameters
$$
D = \left(\frac{8fLQ^2}{\pi^2g\,h_f}\right)^{1/5}
$$
$$
D_B = \left(\frac{8(0.024)(5500)(0.24)^2}{\pi^2(9.81)(17.87)}\right)^{1/5} = 0.5119\ \text{m} \approx 512\ \text{mm}
$$
$$
D_C = \left(\frac{8(0.024)(3000)(0.24)^2}{\pi^2(9.81)(12.35)}\right)^{1/5} = 0.4883\ \text{m} \approx 488\ \text{mm}
$$

**Answer:** Diameter of the branch to B $\approx 512$ mm; diameter of the branch to C $\approx 488$ mm (head at J is 5.75 m above the junction level).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. With f = 0.024 what is the head at J above J's level?
   A. 19.25 m
   B. 25 m
   C. 5.75 m
   D. 4.94 m
   Answer: C. h_f = 19.25 m, so H_J = 25 - 19.25 = 5.75 m. (Key point: Main pipe head loss)

2. Branch B reservoir is 12.125 m below J. What head is available for branch B?
   A. 6.375 m
   B. 17.87 m
   C. 5.75 m
   D. 12.125 m
   Answer: B. h_B = 5.75 + 12.125 = 17.87 m. (Key point: Head available to branches)

3. Why are the diameters (512 and 488 mm) smaller than with f = 0.025?
   A. Lower f gives less friction loss, so smaller pipes suffice and more head is left at J
   B. Lower f needs bigger pipes
   C. The flow rate is smaller
   D. The slopes changed
   Answer: A. Less loss in the main pipe leaves more head, and lower f reduces loss per unit diameter. (Key point: Effect of lower f)

## Close variants set in other exams

- [Branch pipe diameters from a single feeder (f 0.025)](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Areservoir-feeds-two-reservoirs-branch-diameters) — Hydraulics, chapter 3, asked 2×

## Related in Hydraulics

- [Branch diameters equal to a 450 mm direct pipe](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Athree-reservoir-abc-equal-discharge-equivalent-pipe) — Hydraulics, chapter 3
- [Three reservoirs with two parallel pipes](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Athree-reservoirs-five-pipes-parallel) — Hydraulics, chapter 3
- [Three reservoirs with 250 mm concrete pipes](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Athree-reservoir-concrete-pipes-flow-rates) — Hydraulics, chapter 3, asked 2×