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​ = 100 mm, v1​ = 2.75 m/sd2​ = 75 mm

Water flows at 2.75 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 = 2.75 m/s
Q = L/s
2.Easy
12d1​ = 200 mm, v1​ = 1.5 m/sd2​ = 100 mm

Water flows at 1.5 m/s through the wide section of the pipe, which has a diameter of 200 mm. Find the volume flow rate Q.

d1 = 200 mmd2 = 100 mmv1 = 1.5 m/s
Q = L/s
3.Medium
v = ?p0​pp0​ − p = 650 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 650 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 650 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 160 kPa

Water flows at 40 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 160 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 40 L/sd1 = 100 mmd2 = 75 mmp2 = 160 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
d1​ = 200 mmd2​ = 150 mm12Δh = 70 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 70 mm. The discharge coefficient is 0.97. 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 = 200 mmd2 = 150 mmΔh = 70 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
C212 m5 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 2 m above the water surface, and the outlet (open to the air) is 5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 40 mmzC = +2 mz2 = −5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 21.6 L/s
  2. 2. Q = 47.12 L/s
  3. 3. v = 32.91 m/s
  4. 4. p1 = 188 kPa
  5. 5. Q = 86.24 L/s
  6. 6. Q = 12.45 L/s

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