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
v = ?h = 7.5 m

An open water tank drains through a small opening in its side. The free surface is 7.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 7.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 100 mm, v1​ = 2 m/sd2​ = 75 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 100 mm. Find the volume flow rate Q.

d1 = 100 mmd2 = 75 mmv1 = 2 m/s
Q = L/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.61h = 2 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 2 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 2 mCd = 0.61g = 9.81 m/s²
Q = L/s
4.Medium
12d1​ = 200 mm, p1​ = 260 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 260 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 260 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
12d1​ = 75 mm, p1​ = 210 kPad2​ = 40 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 5 m. At section 1 the pressure is 210 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 210 kPav1 = 2 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C210.5 m4.5 md = 40 mmQ = ?

A hose with an inner diameter of 40 mm siphons water from an open tank. The highest point C of the hose is 0.5 m above the water surface, and the outlet (open to the air) is 4.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 40 mmzC = +0.5 mz2 = −4.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v = 12.13 m/s
  2. 2. Q = 15.71 L/s
  3. 3. Q = 1.876 L/s
  4. 4. p2 = 258.1 kPa
  5. 5. p2 = 138.2 kPa
  6. 6. Q = 11.81 L/s

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