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
v = ?h = 2.5 m

An open water tank drains through a small opening in its side. The free surface is 2.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 2.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d = 80 mm, v = 1.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.25 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.25 m/sd = 80 mm
ṁ = kg/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 100 mm, p2​ = 50 kPa

Water flows at 33 L/s through a horizontal pipe that narrows from 150 mm to 100 mm. The pressure in the narrow section is 50 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 33 L/sd1 = 150 mmd2 = 100 mmp2 = 50 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
Q = ?d = 30 mm, Cd​ = 0.64h = 1.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 1.5 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 1.5 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 100 mm, p1​ = 180 kPad2​ = 75 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 75 mm while rising 1 m. At section 1 the pressure is 180 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 75 mmp1 = 180 kPav1 = 2.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 150 mm, p1​ = 170 kPad2​ = 50 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 150 mm to 50 mm while rising 9 m. At section 1 the pressure is 170 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 50 mmp1 = 170 kPav1 = 0.75 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 7.004 m/s
  2. 2. ṁ = 7.917 kg/s
  3. 3. p1 = 57.08 kPa
  4. 4. Q = 2.454 L/s
  5. 5. p2 = 163.4 kPa
  6. 6. p2 = 59.21 kPa

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