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 = 39 L/sv = 3 m/s, d = ?

A water line must carry 39 L/s. To limit noise and wear, the mean velocity should be 3 m/s. Find the inner pipe diameter d needed.

Q = 39 L/sv = 3 m/s
d = mm
2.Easy
v = ?h = 1.5 m

An open water tank drains through a small opening in its side. The free surface is 1.5 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 1.5 mg = 9.81 m/s²
v = m/s
3.Medium
Q = ?d = 20 mm, Cd​ = 0.6h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.6. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 1 mCd = 0.6g = 9.81 m/s²
Q = L/s
4.Medium
v = ?p0​pp0​ − p = 1000 Pastagnation point

A pitot-static tube in a wind tunnel reads a difference of 1000 Pa between the stagnation pressure and the static pressure. The air density is 1.2 kg/m³. Find the air speed v.

p0 − p = 1000 Paρ = 1.2 kg/m³
v = m/s
5.Hard
C210.5 m2 md = 20 mmpC​ = ?

A hose with an inner diameter of 20 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 2 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 = 20 mmzC = +0.5 mz2 = −2 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
12d1​ = 100 mm, p1​ = 200 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 100 mm to 50 mm while rising 1 m. At section 1 the pressure is 200 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 100 mmd2 = 50 mmp1 = 200 kPav1 = 1.25 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. d = 128.7 mm
  2. 2. v = 5.425 m/s
  3. 3. Q = 0.8349 L/s
  4. 4. v = 40.82 m/s
  5. 5. pC = 76.78 kPa
  6. 6. p2 = 178.5 kPa

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