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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
12d = 100 mm, v = 4 m/sṁ = ?

Oil (ρ = 880 kg/m³) flows at 4 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 880 kg/m³v = 4 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 75 mm, v1​ = 2 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 2 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 2 m/s
v2 = m/s
3.Medium
12d1​ = 100 mm, p1​ = 380 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 380 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 380 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 260 kPa

Water flows at 15 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 260 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 15 L/sd1 = 100 mmd2 = 75 mmp2 = 260 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 210 kPad2​ = 25 mm, p2​ = ?Δz = 10 m

Water flows up through a pipe that narrows from 75 mm to 25 mm while rising 10 m. At section 1 the pressure is 210 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 25 mmp1 = 210 kPav1 = 0.5 m/sΔz = 10 mρ = 1000 kg/m³
p2 = kPa
6.Hard
d1​ = 250 mmd2​ = 125 mm12Δh = 140 mmmercuryQ = ?

A horizontal venturi meter (inlet 250 mm, throat 125 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 140 mm. The discharge coefficient is 0.99. 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 = 250 mmd2 = 125 mmΔh = 140 mmCd = 0.99ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 27.65 kg/s
  2. 2. v2 = 4.5 m/s
  3. 3. p2 = 379.7 kPa
  4. 4. p1 = 263.9 kPa
  5. 5. p2 = 101.9 kPa
  6. 6. Q = 73.82 L/s

Full step-by-step solutions: practise this topic on examproblems.com.