All Solutions
Page 428: Practice Problems
– The density of the fluid $rho = 920 ; frac{text{kg}}{text{m}^3}$
– The pressure at the top of the box $P_1 = 105.0text{ kPa}$
– The atmosphere pressure $P_{text{atm}} = 101.3text{ kPa}$
The pressure at a given depth can be found as follows:
$$
begin{equation*}
P(h) – P_{text{atm}} + rho , g , h
end{equation*}
$$
For the top of the box $h = d , P(h) = P_1$:
$$
begin{equation*}
P_1 = P_{text{atm}} + rho , g , d
end{equation*}
$$
Rearranging for $d$:
$$
begin{equation*}
d = frac{P_1 – P_{text{atm}}}{rho , g}
end{equation*}
$$
Plugging in the numbers we have:
$$
begin{align*}
d &= frac{105.0text{ kPa} – 101.3text{ kPa}}{920 ; frac{text{kg}}{text{m}^3} cdot 9.81 ; frac{text{m}}{text{s}^2}} \
d &approx 0.00041text{ m}
end{align*}
$$
$$
p=p_{atm} + rho g d =2.27 text{ MPa}.
$$
$$
P = P_{atmospheric} + rho gh
$$
$$
h = dfrac{P – P_{atmospheric}}{rho g} = dfrac{1.21 times 10^5 Pa – 1.01 times 10^5 Pa}{(796 kg/m^3)(9.81m/s^2}
$$
$$
h = 2.56m
$$
h = 2.56m
$$
$$
p=p_{atm} + rho g d
$$
which yields
$$
d=frac{p-p_{atm}}{rho g} = 2.56text{ m}.
$$