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 = 6 L/sv = 2 m/s, d = ?

A water line must carry 6 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 6 L/sv = 2 m/s
d = mm
2.Easy
12d = 50 mm, v = 1.25 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.25 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.25 m/sd = 50 mm
ṁ = kg/s
3.Medium
12d1​ = 100 mm, p1​ = 400 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 400 kPa and the velocity is 0.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 400 kPav1 = 0.5 m/sρ = 1000 kg/m³
p2 = kPa
4.Medium
12d1​ = 75 mm, p1​ = 310 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 75 mm to 50 mm. In the wide section the pressure is 310 kPa and the velocity is 1.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 310 kPav1 = 1.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C211 m4 md = 40 mmQ = ?

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 4 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 40 mmzC = +1 mz2 = −4 mg = 9.81 m/s²
Q = L/s
6.Hard
H = ?d1​ = 50 mmp1​ = 140 kPad2​ = 30 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 50 mm and a gauge pressure of 140 kPa. The nozzle exit diameter is 30 mm, and the height difference across the nozzle is negligible. Ignoring losses and air resistance, find the height H the jet rises above the nozzle. Use g = 9.81 m/s².

d1 = 50 mmp1 = 140 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. d = 61.8 mm
  2. 2. ṁ = 3.093 kg/s
  3. 3. p2 = 398.1 kPa
  4. 4. p2 = 305.4 kPa
  5. 5. Q = 11.13 L/s
  6. 6. H = 16.4 m

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