import marimo __generated_with = "0.20.4" app = marimo.App(width="medium") @app.cell def _(mo): temp_range = mo.ui.range_slider(start=10, stop=100, step=5, value=(10, 60), show_value=True, label="Temperature range in chart (℃)") #temp_range return (temp_range,) @app.cell def _(mo, temp_range): T_current = mo.ui.slider( start=temp_range.value[0], stop=temp_range.value[-1], step=0.1, show_value=True, label="Current temperature (℃)", ) #T_current return (T_current,) @app.cell def _(H_sat, T_current, mo): H_current = mo.ui.slider( start=1e-6, stop=H_sat(T_current.value), step=5e-5, show_value=True, label="Current humidity $H$", ) #H_current show_switch = mo.ui.switch(value=False, label="Display solution?") return H_current, show_switch @app.cell def _(H_current, T_current, mo, show_switch, temp_range): mo.hstack([temp_range, T_current, H_current, show_switch], wrap=True, align="start") return @app.cell def _( H_current, T_current, display_plot, mo, show_point, show_switch, temp_range, ): ax = display_plot(T_min=temp_range.value[0], T_max=temp_range.value[1]) if show_switch.value: ax, summary = show_point(ax, T=T_current.value, H=H_current.value) display = mo.hstack([summary, ax], widths=[1, 3]) else: display = ax display return @app.cell def _( H_sat, adiabatic_from_Tw, adiabatic_from_enthalpy, enthalpy, fsolve, mo, np, plt, pvap_water, ): def display_plot(T_min=10, T_max=60): fig, ax = plt.subplots(figsize=(8, 5)) T = np.linspace(T_min, T_max, 100) Hs = H_sat(T) ax.xaxis.set_major_locator(plt.MultipleLocator(10.0)) ax.xaxis.set_minor_locator(plt.MultipleLocator(1.0)) ax.yaxis.set_major_locator(plt.MultipleLocator(0.01)) ax.yaxis.set_minor_locator(plt.MultipleLocator(0.005)) ax.grid(True, alpha=0.85, which="major", lw=1.0) ax.grid(True, alpha=0.5, which="minor", lw=0.75) # ax.set_yticks(np.arange(0.01, 0.14001, 0.01)) ax.plot(T, Hs, lw=1.5, color="0.10") ax.text(T[-1] * 1.01, Hs[-1], s=r"$H_p = 100$%", ha="left", va="center") hp = np.array([0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90]) for i_, hp_ in enumerate(hp): H_ = Hs * hp_ ax.plot( T, H_, lw=0.75, color="tab:orange", alpha=0.65, label="Percentage Humidity" if i_ == 0 else None, ) ax.text( T_max * 1.01, H_[-1], s=f"{int(hp_ * 100):0d}%", ha="left", va="center", ) for i_, T_ in enumerate(np.arange(T_min, T_max + 1, 5)): tt = np.linspace(T_, T_max + 10, 100) hh = adiabatic_from_Tw(T_, tt) ax.plot( tt, hh, color="tab:blue", alpha=0.65, lw=0.75, label="Adiabatic sat. curve" if i_ == 0 else None, ) # ax.set_box_aspect(1) ax.set_xlabel("$T$ (℃)") ax.set_ylabel("$H$ (absolute humidity)") ax.set_xlim(T_min, T_max) ax.set_ylim(0, Hs[-1] * 1.05) ax.legend(loc=0) # ax.minorticks_on() fig.tight_layout() # fig.savefig("./psychrometric.png", dpi=250) return ax def show_point(ax, T, H, T_min=10, T_max=60): """Display the current point, and adiabatic line, const concentration line etc """ Hs = H_sat(T) Hy = enthalpy(H, T) assert H < Hs Hp = H / Hs pvap = pvap_water(T) pa = 101.325 / (0.622 / H + 1) HR = pa / pvap ax.plot(T, H, "o", color="black") # The constant T curve ax.plot([T, T], [0, Hs], color="tab:brown", alpha=0.8) # The constant Hs curve (T_dew,) = fsolve(lambda T: H - H_sat(T), T) ax.plot([T_dew, 100], [H, H], color="tab:brown", alpha=0.8) # The adiabatic curve T_test = np.linspace(T_min, T_max, 1000) H_test = adiabatic_from_enthalpy(Hy, T_test) Hs_test = H_sat(T_test) cond = np.where(H_test <= Hs_test) T_w = T_test[cond][0] ax.plot(T_test[cond], H_test[cond], color="tab:brown", alpha=0.8) summary_md = mo.md(f""" ### Current state summary - $T_d = {T:.2f}~^\\circ\\mathrm{{C}}$ - $H = {H:.6f}~\\mathrm{{kg\\ water/kg\\ dry\\ air}}$ - $T_w = {float(T_w):.2f}~^\\circ\\mathrm{{C}}$ - $T_{{dew}} = {float(T_dew):.2f}~^\\circ\\mathrm{{C}}$ - $H_p = {Hp * 100:.1f}\\%$ - $H_R = {100 * HR:.1f}\\%$ - $Hy = {Hy:.2f}~\\mathrm{{kJ/kg\\ dry\\ air}}$ """) return ax, summary_md return display_plot, show_point @app.cell def _(UnivariateSpline, np): _T_C = np.array([0, 10, 20, 25, 30, 40, 50, 60, 70, 80, 90, 100], dtype=float) _P_kPa = np.array( [ 0.611, 1.228, 2.338, 3.168, 4.242, 7.375, 12.333, 19.92, 31.16, 47.34, 70.10, 101.325, ], dtype=float, ) def pvap_water(T): """Get the vapour pressure of water by T T is celsius """ spline = UnivariateSpline(_T_C, _P_kPa, s=0) return spline(T) def H_abs(p, pT=101.325): """Give absolute humidity H as p in kPa""" return 0.622 * p / (pT - p) def H_sat(T, pT=101.325): return H_abs(p=pvap_water(T), pT=pT) def cs(H): """Return humid heat in kJ / kg / K""" return 1.005 + 1.88 * H def enthalpy(H, T): """Return enthalpy of gas in kJ / kg""" return cs(H) * T + 2501.4 * H def adiabatic_from_enthalpy(Hy, T): """return the adiabatic line for give Ts Use the form H(T) = \frac{Hy - 1.005T}{2501.4 + 1.88T} and H is from entlapy of Hs at Tw """ H = (Hy - 1.005 * T) / (2501.4 + 1.88 * T) return H def adiabatic_from_Tw(Tw, T): """return the adiabatic line for give Ts Use the form H(T) = \frac{Hy - 1.005T}{2501.4 + 1.88T} and H is from entlapy of Hs at Tw """ assert np.all(T >= Tw) Hs = H_sat(Tw) Hy = enthalpy(Hs, Tw) H = (Hy - 1.005 * T) / (2501.4 + 1.88 * T) return H return ( H_sat, adiabatic_from_Tw, adiabatic_from_enthalpy, enthalpy, pvap_water, ) @app.cell def _(): import matplotlib.pyplot as plt import numpy as np from scipy.interpolate import UnivariateSpline from scipy.optimize import fsolve return UnivariateSpline, fsolve, np, plt @app.cell def _(): import marimo as mo return (mo,) @app.cell def _(): return if __name__ == "__main__": app.run()