Mechanical Reasoning Guide

Tanks & Pipes

Water finds its own level and flows at the rate its pipes allow. Mechanical aptitude tests ask what it does next. Can you tell?

The valve between B and C opens. How high does the water settle?

Eight rules are all it takes. Read on, then try the test.

Where it appears

Questions about water in tanks and pipes belong to mechanical reasoning (or mechanical comprehension) tests, beside the gears, levers and pulleys. Each shows a picture and asks what happens next. You will meet them in:

Bennett Mechanical Comprehension TestThe classic test of mechanical understanding, used in hiring for technical and engineering roles. Water and pipes are among its everyday-physics topics.

Differential Aptitude Tests (DAT)Its Mechanical Reasoning subtest, used in school and career guidance.

ASVABThe Mechanical Comprehension section of the US military's entrance test.

Technician and apprenticeship testsMechanical aptitude tests for maintenance, manufacturing and trade roles, and the mechanical sections of employers' aptitude batteries.

Those tests usually give a picture with no numbers to count and no time to spare. Here every picture carries its numbers, so each answer is exact, and the questions grow harder as you get better. It trains the habit those questions reward: find the quantity that is kept (the water), then share it out.

Filling a tank: four rules

Every tank shows what it holds when full, and what it has now. Taps (a pipe from above, with its flow in litres a minute) fill it; drains (a pipe on the side, in coral) empty it. The question is how long until the tank is full, or which of four tanks is full first.

1Count the litres still needed

Take what is already in the tank away from what it holds. The time is that, divided by the flow.

time = (holds − has) ÷ flow

The commonest slip: dividing the whole tank's capacity and forgetting the water already in it. That is the time for an empty tank.

60 L still to go, 5 L every minute: 12 minutes

2Taps add

Two taps running at once deliver the sum of their flows, so the tank fills faster than with either one alone.

flow = tap + tap

Do not count only the bigger tap. Both are open.

10 + 5 = 15 L/min, and 75 L to go: 5 minutes

3A drain takes away

While the taps put litres in, the drain lets litres out. The tank only gains the difference.

net flow = taps − drains

A drain is never added to a tap. And do not forget it: ignoring the drain gives a time that is too short.

12 in, 8 out: the tank gains 4 L/min, so 40 L takes 10 minutes

4A split pipe halves

A pipe that splits in two sends half of its flow along each branch. A tank on a branch fills at half the pipe's flow, not the whole of it.

Giving a tank the pipe's whole flow is the slip. The question may ask about either tank, and the two take different times.

20 L/min splits in 10 + 10: tank A needs 100 L, so 10 minutes

Which tank is full first?

Four tanks, each with its own tap (and, higher up, drains). Do not guess from the picture: work out every tank's time with rules 1–3, then pick the smallest.

Two traps in every question: the tank with the fastest tap and the smallest tank. In the test neither is ever the answer. A fast tap on a big tank is slow, and a small tank on a slow tap is slow too.

At the top level some tanks are part full and have drains, and a tank that would win if the drains were ignored is another trap. The winner is always clearly quicker than the next, so careful arithmetic wins.

12, 10, 14 and 8 minutes: D is first, though B has the fastest tap and A is the smallest

Joined tanks: four rules

Tanks stand side by side on a grid of 1 m squares, all equally deep. A pipe with a valve joins their bottoms. A red valve is shut; when the question says it opens, the water runs until the surfaces are level. The question is how high the water settles, or how far one tank rises.

5Joined tanks share one level

Water runs from the higher surface to the lower until they are level, whatever the tanks' sizes or shapes. With two tanks of the same width that is halfway between the two levels.

8 m and 0 m, equal tanks: both settle at 4 m

6All the water, over all the width

No water is lost, so count it first: each tank holds width × height squares of water. Then spread the total over the combined width of the joined tanks.

level = squares of water ÷ total width

The commonest slip: averaging the two levels. A narrow tank holds little water, so it barely changes the level. The average of 8 and 0 is 4, but here the answer is 6.

3 × 8 = 24 squares over a width of 3 + 1 = 4: 6 m

7Only joined tanks count

A tank behind a shut valve takes no part. Look at which valve opens and leave out every tank it does not reach.

Counting the shut-off tank too is the slip. Here only A and B are joined: tank C stays at 2 m and takes no part.

A and B: 2 × 6 + 1 × 9 = 21 squares over a width of 3: 7 m

8The order of the valves does not matter

When the left valve opens and then the right one, the water settles twice. Do not average the first level with the last tank: once both valves are open, the three tanks are one body of water, and the answer is all the water over all the width.

Sometimes a question asks about how far a tank rises. The tank that rises is the lower one: its rise is the settled level minus its own starting level. Do not give the settled level, and do not give how far the other tank falls, because a wider tank falls less for the same water.

First valve: 7 m. Both open: 30 squares over a width of 6 is 5 m

Two questions, solved

1A filling question

Which tank is full first?

The question

Try it first, then open the answer.

Show the answer: tank C

Work out every tank's time: the litres still needed over the net flow.
A needs 170 L at 17 L/min: 10 min.
B needs 130 L at 13 L/min: 10 min.
C needs 50 L at 10 L/min: 5 min.
D needs 40 L at 5 L/min: 8 min.
C is full first, in 5 min.
The traps: A has the fastest tap; D is the smallest tank, but each takes longer.

The other options, and the slip each one is:

A The fastest tap, but its tank takes longer (10 min)B Takes longer (10 min)D The smallest tank, but it takes longer (8 min)

The working, on the picture

2A joined-tanks question

The valve between B and C opens. How high does the water settle?

The question

Try it first, then open the answer.

Show the answer: 8 m

Only the tanks the valve joins share their water: B and C. Tank A stays as it is and does not count.
Count the water in squares, width × height for each tank: 1×2 + 3×10 = 32 squares.
Spread over the joined width, 1 + 3 = 4 m: 32 ÷ 4 = 8 m.

The other options, and the slip each one is:

6 m The average of the levels, the widths ignored9 m Not the level the water settles at10 m The higher of the levels

The working, on the picture

How the practice test runs

3:00 on the clock, and it only runs while a question is on screen.
Levels: each question is a filling question or a joined-tanks question, drawn half and half. Filling climbs from an empty tank and one tap, to a tank part full, two taps, a tap and a drain, four tanks to compare, a split pipe, and four part-full tanks with drains. Joined tanks climb from two equal tanks, to different widths, two part-full tanks, how far a tank rises, three tanks, a valve that joins only some of them, and valves opened one after the other.
The ladder: until your first miss, every right answer jumps a whole level; after it, three right answers in a row jump a level and a miss drops one. Your level carries over to your next session.
Scoring: a right answer earns the question's points (harder questions pay more), a wrong one costs half as many, so guessing does not pay.
Every question is new, and the review after a session works every answer out on its picture and names the slip behind each wrong option.

Try the Tanks & Pipes test

Free and adaptive, no account needed. Start with one tap and an empty tank and climb to drains, split pipes and valves.

Start the Tanks & Pipes test