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
12d = 150 mm, v = 4 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 4 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 4 m/sd = 150 mm
ṁ = kg/s
2.Easy
12Q = 6 L/sv = 2.5 m/s, d = ?

A water line must carry 6 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 6 L/sv = 2.5 m/s
d = mm
3.Medium
12d1​ = 200 mm, p1​ = 380 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 75 mm. In the wide section the pressure is 380 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 75 mmp1 = 380 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
v = ?p0​pp0​ − p = 1400 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1400 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1400 Paρ = 1.2 kg/m³
v = m/s
5.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 230 mmmercuryQ = ?

A horizontal venturi meter (inlet 100 mm, throat 50 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 230 mm. The discharge coefficient is 0.96. 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 = 50 mmΔh = 230 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
C213 m2.5 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 3 m above the water surface, and the outlet (open to the air) is 2.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 20 mmzC = +3 mz2 = −2.5 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 70.69 kg/s
  2. 2. d = 55.28 mm
  3. 3. p2 = 280.9 kPa
  4. 4. v = 48.3 m/s
  5. 5. Q = 14.68 L/s
  6. 6. Q = 2.2 L/s

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