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 = 1.75 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 1.75 m/s through a pipe with an inner diameter of 50 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.75 m/sd = 50 mm
ṁ = kg/s
2.Easy
12Q = 14 L/sv = 2 m/s, d = ?

A water line must carry 14 L/s. To limit noise and wear, the mean velocity should be 2 m/s. Find the inner pipe diameter d needed.

Q = 14 L/sv = 2 m/s
d = mm
3.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 29 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure at the inlet is 29 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 29 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 75 mm, p1​ = 340 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 340 kPa and the velocity is 2 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 340 kPav1 = 2 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
d1​ = 200 mmd2​ = 100 mm12Δh = 400 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 100 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 400 mm. The discharge coefficient is 0.97. Find the flow rate Q. Use ρ = 1000 kg/m³ for water, 13 600 kg/m³ for mercury and g = 9.81 m/s².

d1 = 200 mmd2 = 100 mmΔh = 400 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 90 kPav = ?d = 50 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 90 kPa. Water leaves through an opening with a diameter of 50 mm, 5 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 90 kPa (gauge)h = 5 md = 50 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. ṁ = 4.33 kg/s
  2. 2. d = 94.41 mm
  3. 3. Q = 61.78 L/s
  4. 4. p2 = 331.9 kPa
  5. 5. Q = 78.24 L/s
  6. 6. v = 16.68 m/s

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