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 = 50 mm, v = 1 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1 m/sd = 50 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 2.75 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 75 mm in diameter. The velocity in the wide section is 2.75 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 2.75 m/s
v2 = m/s
3.Medium
12d1​ = 100 mm, p1​ = 130 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 130 kPa and the velocity is 1.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 130 kPav1 = 1.25 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 20 mm, Cd​ = 0.6h = 5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 5 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 = 5 mCd = 0.6g = 9.81 m/s²
Q = L/s
5.Hard
12d1​ = 75 mm, p1​ = 210 kPad2​ = 50 mm, p2​ = ?Δz = 1 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 1 m. At section 1 the pressure is 210 kPa and the velocity is 2.5 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 210 kPav1 = 2.5 m/sΔz = 1 mρ = 1000 kg/m³
p2 = kPa
6.Hard
C212.5 m4 md = 50 mmQ = ?

A hose with an inner diameter of 50 mm siphons water from an open tank. The highest point C of the hose is 2.5 m above the water surface, and the outlet (open to the air) is 4 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 50 mmzC = +2.5 mz2 = −4 mg = 9.81 m/s²
Q = L/s

Answer key

  1. 1. ṁ = 2.474 kg/s
  2. 2. v2 = 11 m/s
  3. 3. p2 = 118.3 kPa
  4. 4. Q = 1.867 L/s
  5. 5. p2 = 187.5 kPa
  6. 6. Q = 17.39 L/s

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