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 = 51 L/sv = 2.5 m/s, d = ?

A water line must carry 51 L/s. To limit noise and wear, the mean velocity should be 2.5 m/s. Find the inner pipe diameter d needed.

Q = 51 L/sv = 2.5 m/s
d = mm
2.Easy
12d1​ = 75 mm, v1​ = 1.75 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 1.75 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 50 mmv1 = 1.75 m/s
v2 = m/s
3.Medium
v = ?p0​pp0​ − p = 1200 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1200 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1200 Paρ = 1.2 kg/m³
v = m/s
4.Medium
12d1​ = 75 mm, p1​ = 370 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 370 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 370 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C211.5 m1 md = 32 mmQ = ?

A hose with an inner diameter of 32 mm siphons water from an open tank. The highest point C of the hose is 1.5 m above the water surface, and the outlet (open to the air) is 1 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 32 mmzC = +1.5 mz2 = −1 mg = 9.81 m/s²
Q = L/s
6.Hard
d1​ = 100 mmd2​ = 50 mm12Δh = 190 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 190 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 = 190 mmCd = 0.96ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. d = 161.2 mm
  2. 2. v2 = 3.938 m/s
  3. 3. v = 44.72 m/s
  4. 4. p2 = 366.8 kPa
  5. 5. Q = 3.562 L/s
  6. 6. Q = 13.34 L/s

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