Question

A pump with a 400 mm diameter suction pipe and 350 mm diameter discharge pipe is to deliver 20,000 litres per minute of 15.60C water. Calculate the pump head in metres if suction gage is 7.5 cm below the pump centreline and reads 127 mmHg vacuum and the discharge gage is 45 cm above the pump centre line and reads 75 kPa.

Answer 1

Answer:

pump head is 10.15 m

Explanation:

given data

diameter suction = 400 mm

diameter discharge = 350 mm

discharge = 20000 l/m

to find out

pump head in meters

solution

we know discharge is 20000 l/m

so discharge = $\frac{1}{3}$ m³/min

and

we know suction head hs  is express as

hs = section gauge × specif gravity of Hg

hs = 0.127 × 13.6

hs = 1.7272 m of water

and

delivery head hd is express as

hd = $\frac{delivery gauge}{density of water*g}$

hd = $\frac{75*10^3}{1000*9.81}$

hd = 7.6453 m of water

and

we know distance between the gauge is here

Distance D = 0.075 + 0.45 = 0.525 m

so

discharge velocity vd is express as

Vd = $\frac{discharge}{area}$

Vd = $\frac{1}{3*\frac{\pi }{4} * 0.35^2}$

Vd = 3.465 m/s

and

suction velocity Vs is express as

Vs = $\frac{discharge}{area}$

Vs =  $\frac{1}{3*\frac{\pi }{4} * 0.4^2}$

Vs = 2.653 m/s

so

pump head will be here

pump head = hs + hd + D + $\frac{Vd^2 - Vs^2}{2g}$

pump head = 1.7272 + 7.6453 + 0.525 +  $\frac{3.465^2 - 2.653^2}{2*9.81}$

so pump head = 10.15 m

Answer 2

The pump head in metres if suction gage is 7.5 cm below the pump centreline and reads 127 mmHg vacuum is; 10.15 m

What is the height of the pump head?

We are given;

Diameter of suction pipe; d_s = 400 mm

Diameter of discharge pipe; d_d= 350 mm

Discharge; Q = 20000 l/min = 0.333 m³/s

Section Gauge = 127 mmHg = 0.127 mHg

Delivery Head = 75 kPa = 75000 N/m²

Formula for delivery head (hd) is;

hd = delivery head/(density of water * acceleration due to gravity:

hd = 75000/(1000 * 9.81)

hd = 7.6453 m

Formula for suction head (hs) is;

hs = section gauge × specific gravity of Hg

hs = 0.127 × 13.6

hs = 1.7272 m of water

Distance between the gauge is;

D = 7.5 cm + 45 cm

D = 52.5 cm = 0.525 m

Discharge velocity is;

V_d = discharge/(π*dd²/4)

V_d = 0.333/(π * 0.35²/4)

V_d = 3.465 m/s

Suction velocity is;

V_s = discharge/(π*ds²/4)

V_s = 0.333/(π * 0.4²/4)

V_s = 2.653 m/s

Pump head is gotten from;

Pump head = hd + hs + D + (V_d² - V_s²)/2g

Pump head = 7.6453 + 1.7272 + 0.525 + (3.465² - 2.653²)/(2*9.81)

Pump head = 10.15 m

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