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 = 28 L/sv = 1 m/s, d = ?

A water line must carry 28 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 28 L/sv = 1 m/s
d = mm
2.Easy
12d1​ = 75 mm, v1​ = 1.25 m/sd2​ = 50 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 50 mmv1 = 1.25 m/s
Q = L/s
3.Medium
d1​ = 200 mmd2​ = 150 mm12p1​ − p2​ = 5 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 150 mm. The pressure at the inlet is 5 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 150 mmp1 − p2 = 5 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 450 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 450 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 450 Paρ = 1.2 kg/m³
v = m/s
5.Hard
C211 m3 md = 40 mmpC​ = ?

A hose with an inner diameter of 40 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 3 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 = 40 mmzC = +1 mz2 = −3 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 150 mm, p1​ = 370 kPad2​ = 100 mm, p2​ = ?Δz = 5 m

Water flows up through a pipe that narrows from 150 mm to 100 mm while rising 5 m. At section 1 the pressure is 370 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 150 mmd2 = 100 mmp1 = 370 kPav1 = 2.75 m/sΔz = 5 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 188.8 mm
  2. 2. Q = 5.522 L/s
  3. 3. Q = 67.59 L/s
  4. 4. v = 27.39 m/s
  5. 5. pC = 62.06 kPa
  6. 6. p2 = 305.6 kPa

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