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 = 0.5 m

An open water tank drains through a small opening in its side. The free surface is 0.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 0.5 mg = 9.81 m/s²
v = m/s
2.Easy
12d1​ = 150 mm, v1​ = 1.25 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 75 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
d1​ = 80 mmd2​ = 40 mm12p1​ − p2​ = 18 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 80 mm and a throat diameter of 40 mm. The pressure at the inlet is 18 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 80 mmd2 = 40 mmp1 − p2 = 18 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 110 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 110 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 110 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 120 kPaQ = ?d = 40 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 120 kPa. Water leaves through an opening with a diameter of 40 mm, 5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 120 kPa (gauge)h = 5 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
C212.5 m4 md = 20 mmQ = ?

A hose with an inner diameter of 20 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 4 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 20 mmzC = +2.5 mz2 = −4 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v = 3.132 m/s
  2. 2. v2 = 5 m/s
  3. 3. Q = 7.787 L/s
  4. 4. p2 = 101.9 kPa
  5. 5. Q = 23.11 L/s
  6. 6. Q = 2.783 L/s

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