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​ = 75 mm, v1​ = 2.5 m/sd2​ = 50 mm

Water flows at 2.5 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 2.5 m/s
Q = L/s
2.Easy
12d1​ = 75 mm, v1​ = 1 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 1 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 230 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 230 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 230 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 11 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 11 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 11 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 50 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 50 mm. The discharge coefficient is 0.95. 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 = 50 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 300 kPad2​ = 25 mm, p2​ = ?Δz = 3 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 3 m. At section 1 the pressure is 300 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 300 kPav1 = 0.5 m/sΔz = 3 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 11.04 L/s
  2. 2. v2 = 2.25 m/s
  3. 3. p2 = 229.5 kPa
  4. 4. Q = 38.05 L/s
  5. 5. Q = 4.335 L/s
  6. 6. p2 = 260.6 kPa

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