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​ = 75 mm, v1​ = 0.5 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 50 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 40 mm in diameter. The velocity in the wide section is 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 40 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 500 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 500 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 500 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = 130 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 40 mm. In the wide section the pressure is 130 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 40 mmp1 = 130 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 200 mmd2​ = 150 mm12Δh = 260 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 260 mm. The discharge coefficient is 0.98. 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 = 260 mmCd = 0.98ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
C212.5 m4.5 md = 50 mmpC​ = ?

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 4.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 50 mmzC = +2.5 mz2 = −4.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa

Answer key

  1. 1. v2 = 1.125 m/s
  2. 2. v2 = 4.395 m/s
  3. 3. v = 28.87 m/s
  4. 4. p2 = 53.88 kPa
  5. 5. Q = 167.9 L/s
  6. 6. pC = 32.63 kPa

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