A Swimmer Under a Lake

Q. A swimmer is 10 m below the surface of a lake. Taking the density of water as 1000 kg/m³, g as 10 m/s² and atmospheric pressure as 1.01 × 10⁵ Pa, what is the pressure on the swimmer, in pascals? expects 2.01 × 10⁵ Pa

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. A swimmer is 10 m $h = 10$ m below the surface of a lake. Taking the density of water as 1000 kg/m³ $ρ = 1000$ kg/m³, g as 10 m/s² $g = 10$ m/s² and atmospheric pressure as 1.01 × 10⁵ Pa $P_{a} = 1.01 \times 10^{5}$ Pa, what is the pressure on the swimmer, in pascals?

The playground

Inputs

depth

h

10.00 m

density

ρ

1000 kg/m³

gravity

g

10 m/s²

atmosphere

P_{a}

1.01e+05 Pa

Outputs

pressure

P

The solution

Solved with PressureAtDepth

Given

$h = 10$ m
$ρ = 1000$ kg/m³
$g = 10$ m/s²
$P_{a} = 1.01 \times 10^{5}$ Pa

Find $P$ .

Working

pressure of the fluid above(swimmer) $P_{g} = ρ \cdot g \cdot h$
$P_{g} = 1000 \cdot 10 \cdot 10$
$P_{g} = 100000$ Pa
pressure adds the surface s(swimmer) $P = P_{a} + P_{g}$
$P = 101000 + 100000$
$P = 201000$ Pa
$P \approx 2.01 \times 10^{5}$ Pato 3 significant figures

Conclusion

The swimmer carries the air above the lake and the water above them too; ten metres of water weighs about as much as the whole atmosphere.

The Ruby

1require_relative "../physics"23question :a_swimmer_under_a_lake do4  kind :numerical5  describes "A swimmer is %{depth} below the surface of a lake. Taking the density of water as %{density}, g as " \6            "%{gravity} and atmospheric pressure as %{atmosphere}, %{pressure}, in pascals?"7  given depth: "10 m"8  given density: "1000 kg/m3"9  given gravity: "10 m/s2"10  given atmosphere: "1.01e5 Pa"11  asks pressure: "what is the pressure on the swimmer"12end

1require_relative "../questions/a_swimmer_under_a_lake"2require_relative "../science/mechanical_properties_of_fluids/pressure_at_depth"34solve :a_swimmer_under_a_lake, using: PressureAtDepth do5  objects :swimmer67  take depth: swimmer.depth8  take density: rho9  take gravity: g10  take atmosphere: P_a1112  pressure = swimmer.pressure13  answer pressure:, in: "Pa", figures: 31415  conclusion "The swimmer carries the air above the lake and the water above them too; ten metres of " \16             "water weighs about as much as the whole atmosphere."17end

1require_relative "../solutions/a_swimmer_under_a_lake"23play_with :a_swimmer_under_a_lake do4  title "A Swimmer Under a Lake"5end

The laws

quantity	written	units	within	from
mass	$m$	kg	0 … ∞	Pressure
gravity	$g$	m/s²	—	Pressure
thrust	$F$	N	—	Pressure
area	$A$	m²	—	Pressure
pressure	$P$	Pa	0 … ∞	Pressure
pressure at the surface	$P_{a}$	Pa	—	PressureAtDepth
density	$ρ$	kg/m³	0 … ∞	PressureAtDepth
depth	$h$	m	—	PressureAtDepth
gauge pressure	$P_{g}$	Pa	—	PressureAtDepth
pressure of ground	$P_{g}$	Pa	0 … ∞
thrust on ground	$F_{g}$	N	—
area of ground	$A_{g}$	m²	—
pressure of swimmer	$P$	Pa	0 … ∞
thrust on swimmer	$F$	N	—
area of swimmer	$A$	m²	—
gauge pressure on ground	$P_{g,g}$	Pa	—
depth of ground	$h_{g}$	m	—
gauge pressure on swimmer	$P_{g}$	Pa	—
depth of swimmer	$h$	m	—
mass of swimmer	$m$	kg	0 … ∞

P_{s} = \frac{F_{s}}{A_{s}}

pressure is force over area

P_{g,p} = ρ \cdot g \cdot h_{p}

pressure of the fluid above

P_{p} = P_{a} + P_{g,p}

pressure adds the surface s

P_{g} = \frac{F_{g}}{A_{g}}

pressure is force over area(ground)

P = \frac{F}{A}

pressure is force over area(swimmer)

P_{g,g} = ρ \cdot g \cdot h_{g}

pressure of the fluid above(ground)

P_{g} = ρ \cdot g \cdot h

pressure of the fluid above(swimmer)

P_{g} = P_{a} + P_{g,g}

pressure adds the surface s(ground)

P = P_{a} + P_{g}

pressure adds the surface s(swimmer)