Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
12d1​ = 100 mm, v1​ = 1.75 m/sd2​ = 40 mm

Water flows at 1.75 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 40 mmv1 = 1.75 m/s
Q = L/s
2.Easy
12d = 80 mm, v = 1.75 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 1.75 m/sd = 80 mm
ṁ = kg/s
3.Medium
12d1​ = 75 mm, p1​ = 350 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 350 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 350 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 180 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 180 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 180 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 210 mmmercuryQ = ?

A horizontal venturi meter (inlet 80 mm, throat 40 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 210 mm. The discharge coefficient is 0.98. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 80 mmd2 = 40 mmΔh = 210 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 360 kPad2​ = 25 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 5 m. At section 1 the pressure is 360 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 360 kPav1 = 1.5 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 13.74 L/s
  2. 2. ṁ = 7.741 kg/s
  3. 3. p2 = 341.9 kPa
  4. 4. p2 = 172.5 kPa
  5. 5. Q = 9.164 L/s
  6. 6. p2 = 220.9 kPa

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