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 = 200 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 200 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 1.25 m/sd = 200 mm
ṁ = kg/s
2.Easy
vd = 15 mmh = 1 m

An open water tank drains through a round opening with a diameter of 15 mm in its side. The free surface is 1 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 1 mg = 9.81 m/s²d = 15 mm
Q = L/s
3.Medium
12d1​ = 150 mm, p1​ = ?d2​ = 100 mm, p2​ = 170 kPa

Water flows at 32 L/s through a horizontal pipe that narrows from 150 mm to 100 mm. The pressure in the narrow section is 170 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 32 L/sd1 = 150 mmd2 = 100 mmp2 = 170 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
Q = ?d = 20 mm, Cd​ = 0.61h = 1 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 20 mm. The water level is kept 1 m above the orifice and the discharge coefficient is 0.61. Find the flow rate Q. Use g = 9.81 m/s².

d = 20 mmh = 1 mCd = 0.61g = 9.81 m/s²
Q = L/s
5.Hard
pair​ = 130 kPaQ = ?d = 20 mmh = 5 m

A closed water tank has compressed air above the water at a gauge pressure of 130 kPa. Water leaves through an opening with a diameter of 20 mm, 5 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 130 kPa (gauge)h = 5 md = 20 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
12d1​ = 75 mm, p1​ = 280 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 8 m. At section 1 the pressure is 280 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 280 kPav1 = 2.25 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. ṁ = 49.48 kg/s
  2. 2. Q = 0.7827 L/s
  3. 3. p1 = 176.7 kPa
  4. 4. Q = 0.8488 L/s
  5. 5. Q = 5.945 L/s
  6. 6. p2 = 191.2 kPa

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