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
12d1​ = 150 mm, v1​ = 1.75 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 100 mm in diameter. The velocity in the wide section is 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 100 mmv1 = 1.75 m/s
v2 = m/s
2.Easy
12d1​ = 75 mm, v1​ = 2 m/sd2​ = 40 mm

Water flows at 2 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 40 mmv1 = 2 m/s
Q = L/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.6h = 2 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 2 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 2 mCd = 0.6g = 9.81 m/s²
Q = L/s
4.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 8 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 8 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 8 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
12d1​ = 150 mm, p1​ = 270 kPad2​ = 100 mm, p2​ = ?Δz = 9 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 9 m. At section 1 the pressure is 270 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 270 kPav1 = 3 m/sΔz = 9 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C213 m3.5 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 3 m above the water surface, and the outlet (open to the air) is 3.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 25 mmzC = +3 mz2 = −3.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 3.938 m/s
  2. 2. Q = 8.836 L/s
  3. 3. Q = 1.181 L/s
  4. 4. Q = 32.45 L/s
  5. 5. p2 = 163.4 kPa
  6. 6. Q = 4.068 L/s

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