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 = 100 mm, v = 1.5 m/sṁ = ?

Water (ρ = 1000 kg/m³) flows at 1.5 m/s through a pipe with an inner diameter of 100 mm. Find the mass flow rate ṁ.

ρ = 1000 kg/m³v = 1.5 m/sd = 100 mm
ṁ = kg/s
2.Easy
12d1​ = 150 mm, v1​ = 1.25 m/sd2​ = 75 mm

Water flows at 1.25 m/s through the wide section of the pipe, which has a diameter of 150 mm. Find the volume flow rate Q.

d1 = 150 mmd2 = 75 mmv1 = 1.25 m/s
Q = L/s
3.Medium
d1​ = 200 mmd2​ = 100 mm12p1​ − p2​ = 27 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 27 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 200 mmd2 = 100 mmp1 − p2 = 27 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 22 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 100 mm and a throat diameter of 50 mm. The pressure at the inlet is 22 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 22 kPaρ = 1000 kg/m³
Q = L/s
5.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 180 mmmercuryQ = ?

A horizontal venturi meter (inlet 80 mm, throat 40 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 180 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 = 80 mmd2 = 40 mmΔh = 180 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 310 kPad2​ = 50 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 7 m. At section 1 the pressure is 310 kPa and the velocity is 2.75 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 310 kPav1 = 2.75 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 11.78 kg/s
  2. 2. Q = 22.09 L/s
  3. 3. Q = 59.61 L/s
  4. 4. Q = 13.45 L/s
  5. 5. Q = 8.398 L/s
  6. 6. p2 = 226 kPa

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