Question 5.8: Calculate the line size and specify the pump required for th...

ODCB density at 20ŽC D 1306 kg / m ^{3}.

Viscosity: 0.9 mNs / m ^{2} (0.9 cp).

Estimation of pipe diameter required

typical velocity for liquid 2 m/s

mass flow =\frac{10,000}{3600}=2.78 kg / s

volumetric flow =\frac{2.78}{1306}=2.13 \times 10^{-3} m ^{3} / s

area of pipe =\frac{\text { volumetric flow }}{\text { velocity }}=\frac{2.13 \times 10^{-3}}{2}=1.06 \times 10^{-3} m ^{2}

diameter of pipe =\sqrt{\left(1.06 \times 10^{-3} \times \frac{4}{\pi}\right)}=0.037 m = 37 mm

Or, use economic pipe diameter formula:

d, optimum =293 \times 2.78^{0.53} \times 1306^{-0.37} = 35.4 mm (5.14)

Take diameter as 40 mm

cross-sectional area =\frac{\pi}{4}\left(40 \times 10^{-3}\right)=1.26 \times 10^{-3} m ^{2}

Pressure drop calculation

Friction loss per unit length, \Delta f_{1}:

R e=\frac{1306 \times 1.70 \times 40 \times 10^{-3}}{0.9 \times 10^{-3}}=9.9 \times 10^{4} (5.5)

Absolute roughness commercial steel pipe, table 5.2 = 0.46 mm

Relative roughness, e/d D 0.046/40 = 0.001

Friction factor from Figure 5.7, f = 0.0027

\begin{aligned}\Delta f_{1} &=8 \times 0.0027 \times \frac{(1)}{\left(40 \times 10^{-3}\right)} \times 1306 \times \frac{1.7^{2}}{2}=1019 N / m ^{2} \\&=1.02 kPa\end{aligned} (5.3)

Design for a maximum flow-rate of 20 per cent above the average flow.

Miscellaneous losses

Take as equivalent pipe diameters. All bends will be taken as 90Ž standard radius elbow.

Line to pump suction:

Control valve pressure drop, allow normal 140 kPa

\left(\times 1.2^{2}\right) maximum 200 kPa

Heat exchanger, allow normal 70 kPa

\left(\times 1.2^{2}\right) maximum 100 kPa

Orifice, allow normal 15 kPa

\left(\times 1.2^{2}\right) maximum 22 kPa

Line from pump discharge:

The line pressure-drop calculation is set out on the calculation sheet shown in Table 5.4.

Pump selection:

differential head, maximum, 44 m

select single-stage centrifugal (Figure 5.6)

Table 5.4. Line calculation form (Example 5.4)
Pump and line calculation sheet
Job no.	Sheet no.	By RKS, 7/7/79			Checked
4415A	1
Fluid		ODCB			DISCHARGE CALCULATION
Temperature °C		20			Line size mm		40
Density kg / m ^{3}		1306				Flow	Norm.	Max.	Units
Viscosity mNs / m ^{2}		0.9			u _{2}	Velocity	1.7	2.0	m/s
Normal flow kg/s		2.78			\Delta f _{2}	Friction loss	1.0	1.5	kPa/m
Design max. flow kg/s		3.34			L _{2}	Line length	54	_	m
					\Delta f _{2} L _{2}	Line loss	54		kPa
SUCTION CALCULATION						Orifice	15	22	kPa
Line size mm		40			30 \%	Control valve	140	200	kPa
	Flow	Norm.	Max.	Units		Equipment
u _{1}	Velocity	1.7	2.0	m/s		(a) Heat ex.	70	100	kPa
\Delta f _{1}	Friction loss	1.0	1.5	kPa/m		(b)	_	_	kPa
L _{1}	Line length	3.4	_	m		(c)	_	_	kPa
\Delta f _{1} L _{1}	Line loss	3.4	5.1	kPa		(6) Dynamic loss	279	403	kPa
\rho u _{1}^{2} / 2	Entrance	1.9	2.7	kPa	Z _{2}	Static head	6.5	_	m
(40 kPa)	Strainer	_	_	kPa	\rho g Z _{2}		85	85	kPa
	(1) Sub-total	5.3	7.8	kPa		Equip. press (max)	200	200	kPa
Z _{1}	Static head	1.5	1.5	m		Contingency	None	None	kPa
\rho gZ _{1}		19.6	19.6	kPa		(7) Sub-total	285	285	kPa
	Equip. press	100	100	kPa	(7) + (6)	Discharge press.	564	685	kPa
	(2) Sub-total	119.6	119.6	kPa	(3)	Suction press.	114.3	111.8	kPa
(2)-(1)	(3) Suction press	114.3	111.8	kPa		(8) Diff. press.	450	576	kPa
	(4) VAP. PRESS.	0.1	0.1	kPa	(8) / \rho g		34	44	m
(3)-(4)	(5) NPSH	114.2	111.7	kPa	Valve/(6)	Control valve % Dyn. Loss	50%
(5) / \rho g		8.7	8.6	m