Engineering
Physics
BernoulIis Equation and Equation of Continuity
Question

Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm–2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube.

(density of water = 1000 kgm–3)

2720 cm3 /s

2420 cm3 /s

3020 cm3 /s

1810 cm3 /s

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Solution

using equation of continuity

            40 VA = 20 VB

Þ         2VA = VB

Using Bernoullies equation

PA+12ρVA2=PB+12ρVB2

⇒     PA−PB=12ρ(VB2−VA2)

 ⇒      ΔP=121000(VB2−VB24)

⇒      ΔP=500×3VB24

⇒         VB=(ΔP)×41500=(700)×41500  m/s

Volume flow rate = 20 × 100 × VB = 2732 cm3/s