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 = 40 mmh = 2.5 m

An open water tank drains through a round opening with a diameter of 40 mm in its side. The free surface is 2.5 m above the opening. Ignoring losses and the contraction of the jet, find the flow rate Q. Use g = 9.81 m/s².

h = 2.5 mg = 9.81 m/s²d = 40 mm
Q = L/s
2.Easy
12d = 80 mm, v = 2 m/sṁ = ?

Seawater (ρ = 1025 kg/m³) flows at 2 m/s through a pipe with an inner diameter of 80 mm. Find the mass flow rate ṁ.

ρ = 1025 kg/m³v = 2 m/sd = 80 mm
ṁ = kg/s
3.Medium
d1​ = 100 mmd2​ = 50 mm12p1​ − p2​ = 32 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 32 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 100 mmd2 = 50 mmp1 − p2 = 32 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
Q = ?d = 30 mm, Cd​ = 0.62h = 2.5 m

Water drains from a large open tank through a sharp-edged orifice with a diameter of 30 mm. The water level is kept 2.5 m above the orifice and the discharge coefficient is 0.62. Find the flow rate Q. Use g = 9.81 m/s².

d = 30 mmh = 2.5 mCd = 0.62g = 9.81 m/s²
Q = L/s
5.Hard
d1​ = 80 mmd2​ = 40 mm12Δh = 220 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 220 mm. The discharge coefficient is 0.95. 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 = 220 mmCd = 0.95ρHg = 13 600 kg/m³g = 9.81 m/s²
Q = L/s
6.Hard
H = ?d1​ = 100 mmp1​ = 80 kPad2​ = 30 mm

A fountain nozzle points straight up. Just below the nozzle the supply pipe has a diameter of 100 mm and a gauge pressure of 80 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 = 100 mmp1 = 80 kPa (gauge)d2 = 30 mmρ = 1000 kg/m³g = 9.81 m/s²
H = m

Answer key

  1. 1. Q = 8.801 L/s
  2. 2. ṁ = 10.3 kg/s
  3. 3. Q = 16.22 L/s
  4. 4. Q = 3.069 L/s
  5. 5. Q = 9.093 L/s
  6. 6. H = 8.222 m

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