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
12d = 100 mm, v = 1.5 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 1.5 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 1.5 m/sd = 100 mm
ṁ = kg/s
2.Easy
vd = 25 mmh = 4 m

An open water tank drains through a round opening with a diameter of 25 mm in its side. The free surface is 4 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 4 mg = 9.81 m/s²d = 25 mm
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 100 mm, p2​ = 60 kPa

Water flows at 38 L/s through a horizontal pipe that narrows from 150 mm to 100 mm. The pressure in the narrow section is 60 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 38 L/sd1 = 150 mmd2 = 100 mmp2 = 60 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 200 mm, p1​ = 240 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 240 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 240 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 150 mmd2​ = 100 mm12Δh = 330 mmmercuryQ = ?

A horizontal venturi meter (inlet 150 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 330 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 = 150 mmd2 = 100 mmΔh = 330 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
d1​ = 200 mmd2​ = 100 mm12Δh = 220 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 220 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 = 200 mmd2 = 100 mmΔh = 220 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 12.08 kg/s
  2. 2. Q = 4.349 L/s
  3. 3. p1 = 69.39 kPa
  4. 4. p2 = 201.3 kPa
  5. 5. Q = 77.61 L/s
  6. 6. Q = 56.83 L/s

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