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
vd = 15 mmh = 7 m

An open water tank drains through a round opening with a diameter of 15 mm in its side. The free surface is 7 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 7 mg = 9.81 m/s²d = 15 mm
Q = L/s
2.Easy
12d = 80 mm, v = 1.25 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 1.25 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 1.25 m/sd = 80 mm
ṁ = kg/s
3.Medium
Q = ?d = 25 mm, Cd​ = 0.65h = 4.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 25 mm. The water level is kept 4.5 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 = 4.5 mCd = 0.65g = 9.81 m/s²
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 2.5 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 75 mmd2 = 50 mmp1 = 340 kPav1 = 2.5 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
pair​ = 150 kPaQ = ?d = 30 mmh = 1 m

A closed water tank has compressed air above the water at a gauge pressure of 150 kPa. Water leaves through an opening with a diameter of 30 mm, 1 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 150 kPa (gauge)h = 1 md = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
d1​ = 200 mmd2​ = 150 mm12Δh = 360 mmmercuryQ = ?

A horizontal venturi meter (inlet 200 mm, throat 150 mm) carries water. A mercury U-tube manometer connected between the inlet and the throat shows a level difference of 360 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 = 150 mmΔh = 360 mmCd = 0.97ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. Q = 2.071 L/s
  2. 2. ṁ = 6.44 kg/s
  3. 3. Q = 2.998 L/s
  4. 4. p2 = 327.3 kPa
  5. 5. Q = 12.64 L/s
  6. 6. Q = 195.6 L/s

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