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 = 3.75 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 3.75 m/s through a pipe with an inner diameter of 150 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 3.75 m/sd = 150 mm
ṁ = kg/s
2.Easy
12d1​ = 200 mm, v1​ = 2 m/sd2​ = 100 mm, v2​ = ?

Water flows through a pipe that narrows from 200 mm to 100 mm in diameter. The velocity in the wide section is 2 m/s. Find the velocity v2 in the narrow section.

d1 = 200 mmd2 = 100 mmv1 = 2 m/s
v2 = m/s
3.Medium
Q = ?d = 40 mm, Cd​ = 0.64h = 6 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 40 mm. The water level is kept 6 m above the orifice and the discharge coefficient is 0.64. Find the flow rate Q. Use g = 9.81 m/s².

d = 40 mmh = 6 mCd = 0.64g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 950 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 950 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 950 Paρ = 1.2 kg/m³
v = m/s
5.Hard
12d1​ = 75 mm, p1​ = 200 kPad2​ = 40 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 40 mm while rising 4 m. At section 1 the pressure is 200 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 40 mmp1 = 200 kPav1 = 2.25 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C210.5 m4.5 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 0.5 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 = 40 mmzC = +0.5 mz2 = −4.5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa

Answer key

  1. 1. ṁ = 66.27 kg/s
  2. 2. v2 = 8 m/s
  3. 3. Q = 8.726 L/s
  4. 4. v = 39.79 m/s
  5. 5. p2 = 132 kPa
  6. 6. pC = 52.25 kPa

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