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
vd = 25 mmh = 0.5 m

An open water tank drains through a round opening with a diameter of 25 mm in its side. The free surface is 0.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 0.5 mg = 9.81 m/s²d = 25 mm
Q = L/s
2.Easy
12d1​ = 150 mm, v1​ = 1 m/sd2​ = 75 mm

Water flows at 1 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 1 m/s
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = 310 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 310 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 310 kPav1 = 1.75 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 17 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 50 mm. The pressure at the inlet is 17 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 17 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 250 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 250 mm. The discharge coefficient is 0.97. 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 = 100 mmd2 = 50 mmΔh = 250 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 9 m. At section 1 the pressure is 200 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 200 kPav1 = 1 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. Q = 1.537 L/s
  2. 2. Q = 17.67 L/s
  3. 3. p2 = 287 kPa
  4. 4. Q = 11.82 L/s
  5. 5. Q = 15.46 L/s
  6. 6. p2 = 104.2 kPa

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