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
12d1​ = 75 mm, v1​ = 0.5 m/sd2​ = 25 mm, v2​ = ?

Water flows through a pipe that narrows from 75 mm to 25 mm in diameter. The velocity in the wide section is 0.5 m/s. Find the velocity v2 in the narrow section.

d1 = 75 mmd2 = 25 mmv1 = 0.5 m/s
v2 = m/s
2.Easy
12d1​ = 150 mm, v1​ = 1.25 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 1.25 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 1.25 m/s
v2 = m/s
3.Medium
12d1​ = 75 mm, p1​ = 140 kPad2​ = 40 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 40 mm. In the wide section the pressure is 140 kPa and the velocity is 1 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 40 mmp1 = 140 kPav1 = 1 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
Q = ?d = 25 mm, Cd​ = 0.65h = 1.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 1.5 m above the orifice and the discharge coefficient is 0.65. Find the flow rate Q. Use g = 9.81 m/s².

d = 25 mmh = 1.5 mCd = 0.65g = 9.81 m/s²
Q = L/s
5.Hard
C212 m5 md = 20 mmQ = ?

A hose with an inner diameter of 20 mm siphons water from an open tank. The highest point C of the hose is 2 m above the water surface, and the outlet (open to the air) is 5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 20 mmzC = +2 mz2 = −5 mg = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 120 kPad2​ = 50 mm, p2​ = ?Δz = 4 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 4 m. At section 1 the pressure is 120 kPa and the velocity is 1.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 120 kPav1 = 1.75 m/sΔz = 4 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 4.5 m/s
  2. 2. v2 = 5 m/s
  3. 3. p2 = 134.3 kPa
  4. 4. Q = 1.731 L/s
  5. 5. Q = 3.112 L/s
  6. 6. p2 = 74.54 kPa

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