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
v = ?h = 1 m

An open water tank drains through a small opening in its side. The free surface is 1 m above the opening. Ignoring losses, find the jet velocity v at the opening. Use g = 9.81 m/s².

h = 1 mg = 9.81 m/s²
v = m/s
2.Easy
12d = 200 mm, v = 3 m/sṁ = ?

Glycerin (ρ = 1260 kg/m³) flows at 3 m/s through a pipe with an inner diameter of 200 mm. Find the mass flow rate ṁ.

ρ = 1260 kg/m³v = 3 m/sd = 200 mm
ṁ = kg/s
3.Medium
v = ?p0​pp0​ − p = 24 kPastagnation point

A pitot-static tube in a water pipe reads a difference of 24 kPa between the stagnation pressure and the static pressure. Find the water velocity v at the tip.

p0 − p = 24 kPaρ = 1000 kg/m³
v = m/s
4.Medium
12d1​ = 100 mm, p1​ = 270 kPad2​ = 50 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 50 mm. In the wide section the pressure is 270 kPa and the velocity is 0.75 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 50 mmp1 = 270 kPav1 = 0.75 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C211.5 m4.5 md = 50 mmQ = ?

A hose with an inner diameter of 50 mm siphons water from an open tank. The highest point C of the hose is 1.5 m above the water surface, and the outlet (open to the air) is 4.5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the flow rate Q.

d = 50 mmzC = +1.5 mz2 = −4.5 mg = 9.81 m/s²
Q = L/s
6.Hard
pair​ = 180 kPaQ = ?d = 25 mmh = 4 m

A closed water tank has compressed air above the water at a gauge pressure of 180 kPa. Water leaves through an opening with a diameter of 25 mm, 4 m below the water surface, into the open air. Ignoring losses, find the flow rate Q. Use g = 9.81 m/s².

pair = 180 kPa (gauge)h = 4 md = 25 mmρ = 1000 kg/m³g = 9.81 m/s²
Q = L/s

Answer key

  1. 1. v = 4.429 m/s
  2. 2. ṁ = 118.8 kg/s
  3. 3. v = 6.928 m/s
  4. 4. p2 = 265.8 kPa
  5. 5. Q = 18.45 L/s
  6. 6. Q = 10.28 L/s

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