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
12Q = 58 L/sv = 2.5 m/s, d = ?

A water line must carry 58 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 58 L/sv = 2.5 m/s
d = mm
2.Easy
v = ?h = 1.5 m

An open water tank drains through a small opening in its side. The free surface is 1.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 1.5 mg = 9.81 m/s²
v = m/s
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 210 kPa

Water flows at 10 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 210 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 10 L/sd1 = 200 mmd2 = 100 mmp2 = 210 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.64h = 4 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 4 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 4 mCd = 0.64g = 9.81 m/s²
Q = L/s
5.Hard
C212.5 m3 md = 50 mmQ = ?

A hose with an inner diameter of 50 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 3 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 50 mmzC = +2.5 mz2 = −3 mg = 9.81 m/s²
Q = L/s
6.Hard
d1​ = 100 mmd2​ = 60 mm12Δh = 120 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 60 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 120 mm. The discharge coefficient is 0.95. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 100 mmd2 = 60 mmΔh = 120 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. d = 171.9 mm
  2. 2. v = 5.425 m/s
  3. 3. p1 = 210.8 kPa
  4. 4. Q = 2.783 L/s
  5. 5. Q = 15.06 L/s
  6. 6. Q = 15.68 L/s

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