You are the maintenance technician on call at a transfer station. A centrifugal pump moving process water is running rough and the discharge gauge is lower than the last inspection sheet recorded. Before ordering parts or calling for a shutdown, you need to check the numbers: flow, pressure, head and efficiency. If the calculations confirm a problem, you will have the evidence needed to schedule the right repair - not a guess.
Why this skill matters
Pump performance math is daily bread for industrial mechanics, marine engineers and water treatment operators. Strong results feed the Industrial Mechanical, Marine and Environmental learning paths.
Learning objectives
Calculate flow rate from volume and time
Convert flow head into pressure (and back)
Compute pump efficiency from hydraulic and electrical power
Recognize classic pump fault signatures like cavitation
Equipment and components
Centrifugal transfer pumpDischarge and suction pressure gaugesFlow meter (magnetic)Electric drive motorStorage tanks and piping
Technical principles
Flow rate is volume moved per unit time
Pressure at the bottom of a column of liquid is rho x g x h
Pump efficiency compares hydraulic power delivered to power consumed
Cavitation is vapor formation at the suction - it sounds like gravel and destroys impellers
How to play
Read each scenario, identify the formula you need, then calculate
Watch your units: litres to cubic metres, minutes to seconds
Compare your answer with the tolerance shown in feedback
Use the explanations to build the habit of checking whether answers make sense
Rules
Each question is worth 10 points plus streak bonuses
Numeric answers are accepted within a small tolerance
A hint reveals the formula (costs 3 points)
Pass each level with 70% or more
Formula and calculation section
Flow Rate
Q = V / t
Flow (m3/s or L/min) = volume moved / time taken.
Hydrostatic Pressure
P = rho x g x h
Pressure from a liquid column: density (kg/m3) x gravity (9.81) x height (m) = pascals.
Pump Efficiency
eta = P_hydraulic / P_input
Hydraulic power delivered divided by shaft/electrical power consumed.
Need help with the mathematics?
Open the relevant mathematics module, practice the calculation, then return to the scenario.
The full game runs on this page - no account, no install. Or open the full-screen play mode with the button above.
Level 1/2Score 0Streak 0Hints 0
Your shift briefing
You are the maintenance technician on call at a transfer station. A centrifugal pump moving process water is running rough and the discharge gauge is lower than the last inspection sheet recorded. Before ordering parts or calling for a shutdown, you need to check the numbers: flow, pressure, head and efficiency. If the calculations confirm a problem, you will have the evidence needed to schedule the right repair - not a guess.
Feedback approach
Every answer includes the full calculation path. Wrong answers show where the numbers went off track, so the next calculation benefits from the correction.
Common mistakes
Mixing litres and cubic metres in flow calculations
Treating gauge pressure as absolute pressure
Ignoring the difference between metres of head and kilopascals
Assuming low discharge pressure means the motor is weak (often it is suction-side trouble)
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Keep learning
Return to the Industrial Mechanical hub to see the full skill path.