Write down the dimensions of the following quantities.
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Velocity
Acceleration
Force
Density (which is mass per unit volume)
Pressure (which is force per unit area)
\end{displayquote}
For a fluid with constant density \(\rho\), the velocity \(v\), pressure \(P\) and height \(h\) at points on a streamline are related by Bernoulli's equation
$$P + \frac { 1 } { 2 } \rho v ^ { 2 } + \rho g h = \mathrm { constant } ,$$
where \(g\) is the acceleration due to gravity.
Show that the left-hand side of Bernoulli's equation is dimensionally consistent.
In a wave tank, a float is performing simple harmonic motion with period 3.49 s in a vertical line. The height of the float above the bottom of the tank is \(h \mathrm {~m}\) at a time \(t \mathrm {~s}\). When \(t = 0\), the height has its maximum value. The value of \(h\) varies between 1.6 and 2.2.
Sketch a graph showing how \(h\) varies with \(t\).
Express \(h\) in terms of \(t\).
Find the magnitude and direction of the acceleration of the float when \(h = 1.7\).