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 m

An open water tank drains through a small opening in its side. The free surface is 7 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 7 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 1 m/s
v2 = m/s
3.Medium
Q = ?d = 40 mm, Cd​ = 0.6h = 3.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 3.5 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 3.5 mCd = 0.6g = 9.81 m/s²
Q = L/s
4.Medium
Q = ?d = 40 mm, Cd​ = 0.65h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 4 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 4 mCd = 0.65g = 9.81 m/s²
Q = L/s
5.Hard
C212.5 m1 md = 25 mmQ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 2.5 m above the water surface, and the outlet (open to the air) is 1 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 25 mmzC = +2.5 mz2 = −1 mg = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 380 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 1 m. At section 1 the pressure is 380 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 380 kPav1 = 2 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v = 11.72 m/s
  2. 2. v2 = 4 m/s
  3. 3. Q = 6.248 L/s
  4. 4. Q = 7.236 L/s
  5. 5. Q = 2.174 L/s
  6. 6. p2 = 362.1 kPa

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