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​ = 200 mm, v1​ = 1 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 75 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 75 mmv1 = 1 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 0.75 m/sd2​ = 50 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 50 mm in diameter. The velocity in the wide section is 0.75 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 50 mmv1 = 0.75 m/s
v2 = m/s
3.Medium
12d1​ = 200 mm, p1​ = 200 kPad2​ = 100 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 200 mm to 100 mm. In the wide section the pressure is 200 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 200 mmd2 = 100 mmp1 = 200 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 100 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 100 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 100 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C211 m2.5 md = 25 mmpC​ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 1 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 absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 25 mmzC = +1 mz2 = −2.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 140 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 140 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 = 140 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v2 = 7.111 m/s
  2. 2. v2 = 3 m/s
  3. 3. p2 = 170 kPa
  4. 4. p2 = 95.43 kPa
  5. 5. pC = 66.97 kPa
  6. 6. Q = 11.45 L/s

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